Heat grill for indirect grilling: Light one side of grill, leaving other side unlit. Close lid; heat grill to 350F.
Meanwhile, cook cola and barbecue sauce in saucepan on medium heat 10 min., stirring occasionally.
Remove from heat; stir in hot sauce. Reserve 3/4 cup sauce to serve with the grilled chicken.
Cut out back bone of chicken carefully with kitchen shears or sharp knife.
Place chicken, skin side up, on work surface; press firmly to flatten.
Place chicken, breast side down, on grill grate over lit area; cover with lid. Grill 15 min.; turn, then place over unlit area. Grill 25 to 30 min. or until chicken is done (165F), monitoring for consistent grill temperature, turning and brushing occasionally with remaining barbecue sauce mixture for the last 15 min.
