Barbecue Chicken Another family favorite is barbecue chicken. This inexpensive meat is easy to barbecue with consistent results. The process for chicken is very similar to other meats. We'll cook both thighs and whole chickens. The thighs we'll marinate overnight, the whole chickens we'll split in half and rub with a BBQ rub. To prepare the thighs, wash well and trim off any excess fat and skin.