Put the chicken in a non-reactive bowl. Combine 2 cups barbecue sauce, the seasoning rub, and vinegar and pour it over the chicken. Cover and marinate the chicken in the refrigerator at least 4 hours, preferably overnight.
Preheat the oven or smoker to 225 degrees F.
Remove the chicken and shake off the excess marinade. If cooking in an oven, place on a rack over a pan to catch drippings. If cooking in a smoker, place directly on a rack. Use your favorite wood, I use New Jersey hickory. Cook until the internal temperature, using an instant-read thermometer, registers 165 degrees F, about 1 1/2 to 2 hours.
Remove the chicken from the rack and place it in a foil pan. Brush with the reserved 1/2 cup barbecue sauce, cover with foil, and place back in the oven or smoker for 1/2 hour. Remove the chicken from the pan and finish off on a grill. Using medium to hot flame, grill until the outer skin is crisp and marked (a few minutes should do it). Serve immediately. You may also place chicken in a clean foil pan and cover with foil to keep warm until serving.
Cook's tip 1: Before adding your wood, make sure the cooking temperature has been achieved. Add meat, then wood. This will prevent the meat from looking too dark.
Cook's tip 2: For a sweeter taste, add 1/4 cup apple juice to your marinade. Adding apple juice to the barbecue sauce while grilling will give it a nice glaze, too.