BusinessInsiderReal Estate Chicken Shack owners planning new restaurant near LSU By Holly Duchmann - December 15, 2020 Chicken Shack chicken is known for its cake-like batter. (File photo) FacebookTwitterLinkedinEmailPrint Joe Delpit, owner of Chicken Shack, considered by many to be Baton Rouge’s longest running restaurant, received a permit late last week to begin construction on a new Highland Road restaurant. Already an INSIDER? Sign in.