Place the chicken pieces in 1 or 2 large resealable plastic bags and add the rest of the ingredients. Shake to mix. Refrigerate at least 1 hour or overnight.
Fire up a grill to medium heat or until the coals are lightly covered with ash. Cook the chicken skin-side up for 20 minutes. Turn and cook an additional 15 to 20 minutes or until the juices run clear when a thigh is pricked with a fork; it should register 180°F on an instant-read thermometer. Alternatively, roast the chicken uncovered in a preheated 400°F oven for 35 to 45 minutes.
Serve half the chicken hot and reserve the rest for another use.