This technique for barbecue chicken makes for a really juicy bird, with a delicious thick glaze of barbecue sauce, without the dreaded burnt skin. Since the chicken is barbecued almost all the way with the skin-side up on the grill, the sauce can cook on to the surface without being burned by the grill's flames.
With a sharp knife, make several deep slashes through the skin and flesh of the chicken; two across the breast, two across the thigh, one across the leg. In a mixing bowl combine the vinegar, garlic. and 1/4 cup of the barbecue sauce. Add the chicken halves and toss to coat in the marinade. Once coated turn the chicken skin-side down in the bowl, cover, and refrigerate for 1-3 hours.
Remove the chicken from the marinade, and pat dry with paper towels.
Mix together the dry rub ingredients and sprinkle over both sides of the chicken.
Build a medium fire in your charcoal grill (you may use a gas grill, but charcoal is recommended for this recipes). Brush the grates lightly with oil, and place the chicken skin-side down on the grill. Cook for just 3-4 minutes to lightly char the skin and create some grill marks, then turn over so the skin side is up. Brush the top of the chicken generously with barbecue sauce. Cover the grill and cook, without turning the chicken again, for 35-40 minutes, or until the internal temp is 165-170 degrees F.
NOTE: While the chicken is grilling, lift the cover every 5 minutes to add more barbecue sauce to the last layer. Since the chicken is cooked all the way with the skin-side up, the sauce will not burn and will build up a nice thick coating of sauce, as the chicken cooks all the way from the bottom up. This is a great way to get juicy meat and beautifully glazed skin without worrying about the chicken turning black.