Hill's Lexington Barbecue Started by Joe Allen Hill in 1951, Hill’s Lexington Barbecue in Winston-Salem is the first to have the name “Lexington Barbecue,” thus their claim to being the “original” Lexington barbecue. At the time they opened there were a few small side street barbecues in Lexington operated by Stamey, Beck and Swicegood. But none called their barbecue place “Lexington Barbecue.