In a medium size bowl, mix together the dry ingredients. Rub the seasoning over the both halves of the chicken. Cover the chicken with plastic wrap and place in the refrigerator for 1 hour.
Place wood chips in the smoking tray of the grill. If you don't have this option you can make a packet out of aluminum foil and punch a few holes in the top of it with a fork and place directly on the hot coals.
Place the chicken on a hot grill over medium-heat with the meat side down. Grill over the wood chips for 1 hour and 20 minutes. Cover, this will keep in the smoke and to prevent oxygen from igniting the smoking wood. After 30 minutes turn the chicken to its opposite side. The juices near the bone should run clear.