Meanwhile, using a flat meat pounder, lightly pound each chicken half to an even thickness of about inch. During the last minute, top each piece with a goat cheese round. Broiled Chicken Bryan: Broil the chicken in a preheated broiler with the rack adjusted about 8 inches from the source of heat. Add the goat cheese about 1 minute before the chicken is done. Tip: Boneless chicken breast is too thin to test correctly with a thermometer, so the touch test works best.