Hey this is a cool fact that I did not know about. Language is really interesting to me. Chai = Tea. I always thought it was a sort of tea but now that I know that it is tea in itself I don't sound ignorant..lol.
You could probably drop the "tea" and just say "chai" and be perfectly well understood. But language is defined by use, not genetics, and the usage is "chai tea," so deal with it.