Why does Australia have no chrome?
There has only been one chromium mine in Australia - the Coobina mine, in the Pilbara region of Western Australia. It is located 80 km south east Newman (23 deg 29' 31" south, 120 deg 16' 32" east). The resource at Coobina is 1.5 Mt @ 29.4% Cr.


  The ore deposit was discovered in 1924 and was once worked under the names of Jimblebah and Murramunda. It was mined as a series of small open cuts for several decades with most of the pits being less than 70 metres deep.


The deposit is associated with an ultramafic unit.


  Chromite deposits in this rock occurs as massive chromite with up to 150 lenses having been mapped so far. The largest around 340 metres long and 6 metres wide.


Chromium clinochlore is mined at Coobina/Jimblebah.

Other deposits of chromite occur at Mount Christie, Tomkinson Ranges and Wingella Hills, in South Australia.

Mount Christie is within the Gawler craton and Tomkinson Ranges and Wingella Hills are within the Musgrave block.

At Moount Christie,


  The best intersection was 1.5 m at 9.8% Cr2O3. Microprobe analysis showed the chromite to contain ~48% Cr2O3 and 30% FeO, which may only be suitable as chemical-grade chromite.
  
  Chromite has been identified within Mesoproterozoic Giles Complex rocks in the far northwest of the State. It occurs as rare veins up to 10 mm thick within layers of pyroxenite in the Tomkinson Ranges (Coats, 1956) and as grains in ultrabasic rocks of the Wingelinna Hills intrusions. A representative sample gave an assay of 16.9% Cr2O3.


Geoscience Australia has very little information about Coobina.

Some more information from Geoscience World and Research Gate.