Reduce the heat to low on a gas grill, or transfer to indirect heat on a charcoal grill. Starting with the chicken skin side up, cover and grill, flipping the chicken every 5 minutes, until cooked through and an instant-read thermometer in the thickest part of the meat not touching bone registers at least 165ºF, 15 to 17 minutes more. In the final minute of cooking, brush the chicken all over with the reserved marinade.
