Caitlyn Jenner -- Check Me Out on Broadway!!! (PHOTO + VIDEO)

Caitlyn Jenner made a very sexy splash on Broadway Tuesday night ... and she's giving Kim a run for her money.

Caitlyn went with transgender actress Candis Cayne to the Broadway show, "An American in Paris."

It's the first time Caitlyn -- who is 65 -- has been out in public with full-on cleavage and lace. It's pretty apparent ... she's been taking Kim's advice on how to dress and especially how to look good in photographs.

When Caitlyn left the theater, a throng of fans were there to greet her.

One thing is clear ... Caitlyn ain't wearin' Bruce's baseball caps anymore.