No, it's not a place where they serve only chicken breasts.
"Breastaurants" refers to dining establishments like Hooters and Twin Peaks, where the focus is on the female form of the server rather than the food being served. I just learned this term this morning when reading a forum about future trends. The contributors to the discussion disheartened me. Not one had anything to say about God. Basically, the prevailing thought was that men like sex and food, so breastaurants will continue to grow in popularity.
I realized what a sheltered life I live.
Maybe it's best for me not to know about future trends.