Preheat an outdoor grill to 350 degrees F (175 degrees C) and lightly oil the grate.

Season each side of the chicken thighs with salt and pepper. Place inner side of each chicken breast on the preheated grill and brush the top of each thigh with 1 tablespoon barbecue sauce. Grill undisturbed for 3 minutes, watching for flare-ups. Move chicken pieces to another part of the grill if flare-ups occur.

Turn chicken pieces and brush each side with an additional 1 tablespoon barbecue sauce. Grill, turning the pieces three more times, until an instant-read thermometer inserted into the center reads at least 165 degrees F (74 degrees C), about 6 minutes per side. Serve with additional sauce.