What does let the chips fall where they may mean?

It's a misquote of the phrase "Let the cards fall where they may" which refers to one's fortune being told by a tarot card reader. The card reader generally asks her client if he has any preference in how she would lay the cards out and this was the usual response.

"Chips" refers to chips of wood. This phrase also uses the image of a person chopping wood and letting the chips fly everywhere instead of trying to be neat and chop on one side so they'll fall in a pile.

At any rate, the idiom means "let things happen the way they are supposed to happen."