What significance and applications does nanotechnology have in chemistry?
There is branch named Chemical Nanoscience and Nanotechnology Which deals with chemistry asspects.

Talking about organic chemistry, nanotechnology is used for Organic synthesis. 

With help of Modern Chemistry today we can synthesis almost all complex molecules, thanks to nanotechnology.

Check out Wikipedia-1, 
Wikipedia-2 and nano.gov



For organic chemistry, Polymer nanotechnology is developed notably.  Polymer matrix and nanocomposites have become a prominent area of current research and development 

Example:

exfoliation