These restaurant chains serve smoky, tender pulled chicken sandwiches that diners recommend. However, if you aren’t a fan of pork, a pulled chicken sandwich is basically the same thing, but made with poultry. Here are 6 restaurant chains with the best pulled chicken sandwiches, according to diners. Famous Dave’sFamous Dave’s offers two BBQ chicken sandwich options, one of which is a BBQ Pulled Chicken Sandwich, roasted, pulled chicken tossed in Rich & Sassy sauce, and topped with melted Monterey Jack cheese. City BarbequeThe City Barbeque Pulled Chicken Sandwich features hickory-smoked chicken pulled from the bone, mixed with scratch-made Alabama white (‘Bama) sauce, and served on a toasted bun.