diff --git a/dask/array/core.py b/dask/array/core.py
--- a/dask/array/core.py
+++ b/dask/array/core.py
@@ -3129,7 +3129,9 @@ def normalize_chunks(chunks, shape=None, limit=None, dtype=None, previous_chunks
                 "Got chunks=%s, shape=%s" % (chunks, shape)
             )
 
-    return tuple(tuple(int(x) if not math.isnan(x) else x for x in c) for c in chunks)
+    return tuple(
+        tuple(int(x) if not math.isnan(x) else np.nan for x in c) for c in chunks
+    )
 
 
 def _compute_multiplier(limit: int, dtype, largest_block: int, result):
diff --git a/dask/array/rechunk.py b/dask/array/rechunk.py
--- a/dask/array/rechunk.py
+++ b/dask/array/rechunk.py
@@ -309,12 +309,13 @@ def rechunk(
     )
 
     # Now chunks are tuple of tuples
-    if not balance and (chunks == x.chunks):
-        return x
     ndim = x.ndim
     if not len(chunks) == ndim:
         raise ValueError("Provided chunks are not consistent with shape")
 
+    if not balance and (chunks == x.chunks):
+        return x
+
     if balance:
         chunks = tuple(_balance_chunksizes(chunk) for chunk in chunks)
 

If using `np.nan` instead of `float("nan")`, this works as expected. Using `np.nan` is mentioned in https://docs.dask.org/en/stable/array-chunks.html#unknown-chunks, but the rechunking tests use `float("nan")` instead (https://github.com/dask/dask/blob/c9a9edef0c7e996ef72cb474bf030778189fd737/dask/array/tests/test_rechunk.py#L615). I'd recommend adjusting the tests to use `np.nan` and coercing any NaN values to `np.nan`.
diff --git a/dask/array/tests/test_array_core.py b/dask/array/tests/test_array_core.py
--- a/dask/array/tests/test_array_core.py
+++ b/dask/array/tests/test_array_core.py
@@ -2949,6 +2949,8 @@ def test_normalize_chunks():
     assert normalize_chunks(10, (30, 5)) == ((10, 10, 10), (5,))
     assert normalize_chunks((), (0, 0)) == ((0,), (0,))
     assert normalize_chunks(-1, (0, 3)) == ((0,), (3,))
+    assert normalize_chunks(((float("nan"),),)) == ((np.nan,),)
+
     assert normalize_chunks("auto", shape=(20,), limit=5, dtype="uint8") == (
         (5, 5, 5, 5),
     )
diff --git a/dask/array/tests/test_rechunk.py b/dask/array/tests/test_rechunk.py
--- a/dask/array/tests/test_rechunk.py
+++ b/dask/array/tests/test_rechunk.py
@@ -282,6 +282,28 @@ def test_rechunk_same():
     assert x is y
 
 
+def test_rechunk_same_unknown():
+    dd = pytest.importorskip("dask.dataframe")
+    x = da.ones(shape=(10, 10), chunks=(5, 10))
+    y = dd.from_array(x).values
+    new_chunks = ((np.nan, np.nan), (10,))
+    assert y.chunks == new_chunks
+    result = y.rechunk(new_chunks)
+    assert y is result
+
+
+def test_rechunk_same_unknown_floats():
+    """Similar to test_rechunk_same_unknown but testing the behavior if
+    ``float("nan")`` is used instead of the recommended ``np.nan``
+    """
+    dd = pytest.importorskip("dask.dataframe")
+    x = da.ones(shape=(10, 10), chunks=(5, 10))
+    y = dd.from_array(x).values
+    new_chunks = ((float("nan"), float("nan")), (10,))
+    result = y.rechunk(new_chunks)
+    assert y is result
+
+
 def test_rechunk_with_zero_placeholders():
     x = da.ones((24, 24), chunks=((12, 12), (24, 0)))
     y = da.ones((24, 24), chunks=((12, 12), (12, 12)))
@@ -368,8 +390,8 @@ def _assert_steps(steps, expected):
 def test_plan_rechunk():
     c = (20,) * 2  # coarse
     f = (2,) * 20  # fine
-    nc = (float("nan"),) * 2  # nan-coarse
-    nf = (float("nan"),) * 20  # nan-fine
+    nc = (np.nan,) * 2  # nan-coarse
+    nf = (np.nan,) * 20  # nan-fine
 
     # Trivial cases
     steps = _plan((), ())
@@ -513,8 +535,8 @@ def test_dont_concatenate_single_chunks(shape, chunks):
 
 
 def test_intersect_nan():
-    old_chunks = ((float("nan"), float("nan")), (8,))
-    new_chunks = ((float("nan"), float("nan")), (4, 4))
+    old_chunks = ((np.nan, np.nan), (8,))
+    new_chunks = ((np.nan, np.nan), (4, 4))
 
     result = list(intersect_chunks(old_chunks, new_chunks))
     expected = [
@@ -527,8 +549,8 @@ def test_intersect_nan():
 
 
 def test_intersect_nan_single():
-    old_chunks = ((float("nan"),), (10,))
-    new_chunks = ((float("nan"),), (5, 5))
+    old_chunks = ((np.nan,), (10,))
+    new_chunks = ((np.nan,), (5, 5))
 
     result = list(intersect_chunks(old_chunks, new_chunks))
     expected = [
@@ -539,8 +561,8 @@ def test_intersect_nan_single():
 
 
 def test_intersect_nan_long():
-    old_chunks = (tuple([float("nan")] * 4), (10,))
-    new_chunks = (tuple([float("nan")] * 4), (5, 5))
+    old_chunks = (tuple([np.nan] * 4), (10,))
+    new_chunks = (tuple([np.nan] * 4), (5, 5))
     result = list(intersect_chunks(old_chunks, new_chunks))
     expected = [
         (((0, slice(0, None, None)), (0, slice(0, 5, None))),),
@@ -603,7 +625,6 @@ def test_rechunk_unknown(x, chunks):
     y = dd.from_array(x).values
     result = y.rechunk(chunks)
     expected = x.rechunk(chunks)
-
     assert_chunks_match(result.chunks, expected.chunks)
     assert_eq(result, expected)
 
@@ -612,7 +633,7 @@ def test_rechunk_unknown_explicit():
     dd = pytest.importorskip("dask.dataframe")
     x = da.ones(shape=(10, 10), chunks=(5, 2))
     y = dd.from_array(x).values
-    result = y.rechunk(((float("nan"), float("nan")), (5, 5)))
+    result = y.rechunk(((np.nan, np.nan), (5, 5)))
     expected = x.rechunk((None, (5, 5)))
     assert_chunks_match(result.chunks, expected.chunks)
     assert_eq(result, expected)
@@ -635,8 +656,8 @@ def test_rechunk_unknown_raises():
 
 
 def test_old_to_new_single():
-    old = ((float("nan"), float("nan")), (8,))
-    new = ((float("nan"), float("nan")), (4, 4))
+    old = ((np.nan, np.nan), (8,))
+    new = ((np.nan, np.nan), (4, 4))
     result = _old_to_new(old, new)
 
     expected = [
@@ -648,8 +669,8 @@ def test_old_to_new_single():
 
 
 def test_old_to_new():
-    old = ((float("nan"),), (10,))
-    new = ((float("nan"),), (5, 5))
+    old = ((np.nan,), (10,))
+    new = ((np.nan,), (5, 5))
     result = _old_to_new(old, new)
     expected = [
         [[(0, slice(0, None, None))]],
@@ -660,8 +681,8 @@ def test_old_to_new():
 
 
 def test_old_to_new_large():
-    old = (tuple([float("nan")] * 4), (10,))
-    new = (tuple([float("nan")] * 4), (5, 5))
+    old = (tuple([np.nan] * 4), (10,))
+    new = (tuple([np.nan] * 4), (5, 5))
 
     result = _old_to_new(old, new)
     expected = [
@@ -677,9 +698,8 @@ def test_old_to_new_large():
 
 
 def test_changing_raises():
-    nan = float("nan")
     with pytest.raises(ValueError) as record:
-        _old_to_new(((nan, nan), (4, 4)), ((nan, nan, nan), (4, 4)))
+        _old_to_new(((np.nan, np.nan), (4, 4)), ((np.nan, np.nan, np.nan), (4, 4)))
 
     assert "unchanging" in str(record.value)
 

Skip rechunk when rechunking to the same chunks with unknown sizes
When rechunking to the same chunks as the input array, we should skip rechunking even if some chunks have an unknown size, i.e., are `nan`.

**Minimal Complete Verifiable Example**:

```python
import dask.array as da
import dask.dataframe as dd
x = da.ones(shape=(10, 10), chunks=(5, 2))
y = dd.from_array(x).values
result = y.rechunk(((float("nan"), float("nan")), (10, )))
assert y is result
```

cc @jrbourbeau 

dask/array/tests/test_rechunk.py::test_rechunk_same_unknown_floats dask/array/tests/test_array_core.py::test_normalize_chunks
dask/array/tests/test_array_core.py::test_normalize_chunks_nan dask/array/tests/test_array_core.py::test_stack_scalars dask/array/tests/test_array_core.py::test_to_dask_dataframe dask/array/tests/test_rechunk.py::test_rechunk_empty_chunks dask/array/tests/test_array_core.py::test_astype dask/array/tests/test_array_core.py::test_meta[dtype1] dask/array/tests/test_array_core.py::test_vindex_basic dask/array/tests/test_array_core.py::test_from_array_with_missing_chunks dask/array/tests/test_array_core.py::test_setitem_extended_API_2d[index11-value11] dask/array/tests/test_array_core.py::test_reshape[original_shape15-new_shape15-2] dask/array/tests/test_array_core.py::test_from_array_scalar[int32] dask/array/tests/test_array_core.py::test_setitem_extended_API_2d[index18-value18] dask/array/tests/test_rechunk.py::test_rechunk_unknown[x5-chunks5] dask/array/tests/test_array_core.py::test_elemwise_uneven_chunks dask/array/tests/test_array_core.py::test_setitem_hardmask dask/array/tests/test_array_core.py::test_broadcast_operator[u_shape3-v_shape3] dask/array/tests/test_array_core.py::test_to_hdf5 dask/array/tests/test_array_core.py::test_matmul dask/array/tests/test_array_core.py::test_map_blocks_block_info_with_new_axis dask/array/tests/test_array_core.py::test_concatenate_unknown_axes dask/array/tests/test_array_core.py::test_to_delayed_optimize_graph dask/array/tests/test_array_core.py::test_concatenate_axes dask/array/tests/test_rechunk.py::test_rechunk_with_zero_placeholders dask/array/tests/test_array_core.py::test_broadcast_to_scalar dask/array/tests/test_rechunk.py::test_rechunk_auto_3d dask/array/tests/test_array_core.py::test_reshape[original_shape31-new_shape31-chunks31] dask/array/tests/test_rechunk.py::test_rechunk_unknown[x8-chunks8] dask/array/tests/test_array_core.py::test_Array_computation dask/array/tests/test_array_core.py::test_store_deterministic_keys[True-False] dask/array/tests/test_rechunk.py::test_balance_split_into_n_chunks dask/array/tests/test_array_core.py::test_chunk_shape_broadcast[1] dask/array/tests/test_array_core.py::test_compute_chunk_sizes_warning_fixes_to_zarr dask/array/tests/test_array_core.py::test_normalize_chunks_tuples_of_tuples dask/array/tests/test_array_core.py::test_broadcast_operator[u_shape4-v_shape4] dask/array/tests/test_array_core.py::test_no_chunks_yes_chunks dask/array/tests/test_array_core.py::test_map_blocks_block_info dask/array/tests/test_array_core.py::test_asanyarray dask/array/tests/test_array_core.py::test_broadcast_to_chunks dask/array/tests/test_array_core.py::test_block_simple_column_wise dask/array/tests/test_array_core.py::test_vindex_negative dask/array/tests/test_array_core.py::test_blockwise_zero_shape_new_axes dask/array/tests/test_array_core.py::test_normalize_chunks_auto_2d[shape2-auto-10-expected2] dask/array/tests/test_array_core.py::test_slice_reversed dask/array/tests/test_array_core.py::test_keys dask/array/tests/test_array_core.py::test_store_compute_false dask/array/tests/test_array_core.py::test_reshape_avoids_large_chunks[shape0-chunks0-reshape_size0-None] dask/array/tests/test_array_core.py::test_reshape[original_shape9-new_shape9-2] dask/array/tests/test_array_core.py::test_map_blocks_with_changed_dimension dask/array/tests/test_array_core.py::test_setitem_extended_API_2d[3-value7] dask/array/tests/test_array_core.py::test_broadcast_against_zero_shape dask/array/tests/test_array_core.py::test_reshape[original_shape28-new_shape28-chunks28] dask/array/tests/test_array_core.py::test_repr_html_array_highlevelgraph dask/array/tests/test_array_core.py::test_repr_meta dask/array/tests/test_rechunk.py::test_rechunk_unknown_explicit dask/array/tests/test_array_core.py::test_chunk_shape_broadcast[3] dask/array/tests/test_array_core.py::test_slicing_with_ellipsis dask/array/tests/test_array_core.py::test_elemwise_with_lists[other0-100] dask/array/tests/test_array_core.py::test_block_with_1d_arrays_column_wise dask/array/tests/test_array_core.py::test_from_array_scalar[uint64] dask/array/tests/test_array_core.py::test_setitem_extended_API_2d[index16--1] dask/array/tests/test_array_core.py::test_block_no_lists dask/array/tests/test_array_core.py::test_delayed_array_key_hygeine dask/array/tests/test_rechunk.py::test_rechunk_with_zero dask/array/tests/test_array_core.py::test_len_object_with_unknown_size dask/array/tests/test_array_core.py::test_setitem_extended_API_2d[index2--1] dask/array/tests/test_array_core.py::test_from_array_scalar[int64] dask/array/tests/test_array_core.py::test_chunked_dot_product dask/array/tests/test_rechunk.py::test_rechunk_avoid_needless_chunking dask/array/tests/test_rechunk.py::test_balance_raises dask/array/tests/test_array_core.py::test_setitem_extended_API_2d[index9-value9] dask/array/tests/test_rechunk.py::test_rechunk_same dask/array/tests/test_array_core.py::test_reshape[original_shape24-new_shape24-6] dask/array/tests/test_rechunk.py::test_rechunk_method dask/array/tests/test_array_core.py::test_from_array_scalar[datetime64] dask/array/tests/test_array_core.py::test_bool dask/array/tests/test_array_core.py::test_from_array_no_asarray[True-False-matrix] dask/array/tests/test_array_core.py::test_normalize_chunks_auto_2d[shape0-chunks0-20-expected0] dask/array/tests/test_array_core.py::test_reshape[original_shape3-new_shape3-12] dask/array/tests/test_array_core.py::test_reshape[original_shape17-new_shape17-3] dask/array/tests/test_array_core.py::test_elemwise_dtype dask/array/tests/test_array_core.py::test_from_array_minus_one dask/array/tests/test_rechunk.py::test_balance_basics_2d dask/array/tests/test_array_core.py::test_map_blocks_with_invalid_drop_axis dask/array/tests/test_rechunk.py::test_rechunk_1d dask/array/tests/test_rechunk.py::test_rechunk_auto_image_stack[1000] dask/array/tests/test_array_core.py::test_setitem_extended_API_2d[index20-value20] dask/array/tests/test_array_core.py::test_3925 dask/array/tests/test_array_core.py::test_memmap dask/array/tests/test_array_core.py::test_slicing_with_object_dtype dask/array/tests/test_array_core.py::test_from_array_scalar[timedelta64] dask/array/tests/test_array_core.py::test_vindex_identity dask/array/tests/test_array_core.py::test_broadcast_operator[u_shape5-v_shape5] dask/array/tests/test_array_core.py::test_graph_from_arraylike[True] dask/array/tests/test_array_core.py::test_from_array_scalar[int] dask/array/tests/test_rechunk.py::test_rechunk_zero_dim_array dask/array/tests/test_array_core.py::test_long_slice dask/array/tests/test_array_core.py::test_reshape[original_shape13-new_shape13-2] dask/array/tests/test_array_core.py::test_field_access_with_shape dask/array/tests/test_array_core.py::test_vindex_errors dask/array/tests/test_array_core.py::test_from_array_scalar[int8] dask/array/tests/test_rechunk.py::test_rechunk_auto_1d[20-chunks4-5-expected4] dask/array/tests/test_array_core.py::test_map_blocks_with_negative_drop_axis dask/array/tests/test_rechunk.py::test_old_to_new_large dask/array/tests/test_rechunk.py::test_balance_chunks_unchanged dask/array/tests/test_array_core.py::test_block_empty_lists dask/array/tests/test_array_core.py::test_broadcast_operator[u_shape1-v_shape1] dask/array/tests/test_array_core.py::test_store_delayed_target dask/array/tests/test_array_core.py::test_align_chunks_to_previous_chunks dask/array/tests/test_rechunk.py::test_rechunk_unknown[x10-chunks10] dask/array/tests/test_array_core.py::test_from_array_scalar[object_] dask/array/tests/test_rechunk.py::test_rechunk_same_unknown dask/array/tests/test_array_core.py::test_regular_chunks[data6] dask/array/tests/test_array_core.py::test_from_array_scalar[int16] dask/array/tests/test_array_core.py::test_h5py_newaxis dask/array/tests/test_array_core.py::test_arithmetic dask/array/tests/test_array_core.py::test_setitem_extended_API_2d[index3--1] dask/array/tests/test_array_core.py::test_from_array_ndarray_getitem dask/array/tests/test_array_core.py::test_from_array_with_lock[True] dask/array/tests/test_array_core.py::test_reshape[original_shape4-new_shape4-12] dask/array/tests/test_array_core.py::test_asarray_h5py[False-asarray] dask/array/tests/test_array_core.py::test_block_tuple dask/array/tests/test_array_core.py::test_no_warnings_from_blockwise dask/array/tests/test_array_core.py::test_setitem_extended_API_2d[index10-value10] dask/array/tests/test_array_core.py::test_from_array_scalar[complex256] dask/array/tests/test_rechunk.py::test_intersect_chunks_with_nonzero dask/array/tests/test_array_core.py::test_getter dask/array/tests/test_array_core.py::test_compute_chunk_sizes dask/array/tests/test_array_core.py::test_reshape[original_shape33-new_shape33-chunks33] dask/array/tests/test_rechunk.py::test_dtype dask/array/tests/test_array_core.py::test_elemwise_with_ndarrays dask/array/tests/test_array_core.py::test_elemwise_differently_chunked dask/array/tests/test_array_core.py::test_setitem_extended_API_2d_rhs_func_of_lhs dask/array/tests/test_array_core.py::test_slice_with_integer_types dask/array/tests/test_array_core.py::test_copy_mutate dask/array/tests/test_array_core.py::test_auto_chunks_h5py dask/array/tests/test_array_core.py::test_store_regions dask/array/tests/test_array_core.py::test_chunk_assignment_invalidates_cached_properties dask/array/tests/test_rechunk.py::test_rechunk_auto_1d[100-100-10-expected2] dask/array/tests/test_rechunk.py::test_balance_2d_negative_dimension dask/array/tests/test_array_core.py::test_constructors_chunks_dict dask/array/tests/test_array_core.py::test_zarr_inline_array[True] dask/array/tests/test_array_core.py::test_setitem_extended_API_0d dask/array/tests/test_array_core.py::test_stack_promote_type dask/array/tests/test_array_core.py::test_from_array_dask_array dask/array/tests/test_array_core.py::test_h5py_tokenize dask/array/tests/test_array_core.py::test_block_mixed_1d_and_2d dask/array/tests/test_array_core.py::test_setitem_extended_API_1d[index2--3] dask/array/tests/test_array_core.py::test_elemwise_on_scalars dask/array/tests/test_array_core.py::test_chunked_transpose_plus_one dask/array/tests/test_array_core.py::test_to_backend dask/array/tests/test_array_core.py::test_reshape[original_shape32-new_shape32-chunks32] dask/array/tests/test_array_core.py::test_setitem_extended_API_1d[index4--4] dask/array/tests/test_array_core.py::test_store_kwargs dask/array/tests/test_array_core.py::test_zarr_regions dask/array/tests/test_array_core.py::test_from_array_tasks_always_call_getter[False-x2-1] dask/array/tests/test_array_core.py::test_elemwise_with_lists[other2-6] dask/array/tests/test_array_core.py::test_np_array_with_zero_dimensions 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