But what if there was a Chick-Fil-A affiliated restaurant that doesn't serve chicken at all? Instead of concentrating on delicious chicken sandwiches, the concept restaurant will concentrate on drinks. Chick-Fil-A Concept Store in Atlanta, GeorgiaA concept store being built in Atlanta, Georgia, will not focus on chicken sandwiches (KXAN). The concept store will not be foodless. This isn't the first time that Chick-Fil-A has opened a spinoff restaurant.