Mix all brine ingredients in a large pot and heat just until the sugar has blended well with the water and other ingredients. Stir often during the heating process. Remove from heat and allow to cool to room temperature, about an hour. Once the brine has cooled, place chicken in a container and pour the brine mixture until the meat is completely covered. Place in the refrigerator for at least two hours or more, allowing the brine to soak into the meat. Keep in mind that the brine will make the meat saltier, so be careful not to over-brine. Remove the chicken from the brine and lightly rinse with cool water. Pat the chicken as dry as possible with a paper towel, and place on a cookie sheet for the dry rub preparation.
Prepare your smoker for indirect heat at 250 degrees and soak 2 cups of wood smoking chips (I prefer Apple wood) in water for at least a half hour. While the smoker is rising to temperature and the wood chips are soaking, prepare to apply the dry rub.
First, brush on a light coating of olive oil onto both sides of the chicken. Next, apply the dry rub to the meat, carefully sprinkling some of the rub under the skin when possible. Remove the smoking chips from the water and pat dry with a towel. Add smoking chips to smoker. Place a drip pan under the surface of where the chicken will be placed and add 2 cups of water or apple juice to the drip pan. Place the chicken on the cooking surface and close the lid. Remember to cook on indirect heat, not directly over the heat source. Carefully maintain temperature between 250-275 degrees for 1 hour and 30minutes, to 1 hour and 45 minutes.
For the Sauce:.
Mix all sauce ingredients in a small pot and bring to a light boil, stirring constantly. Remove from heat and allow to cool. Brush on a small amount of sauce during the final 1/2 hour of smoking and allow the chicken to finish cooking.
After smoking at a temperature of 250-275 degrees for 1 1/2 hours check the meat for doneness, 170 degrees is a good final temperature. Remove from heat and allow to rest for 10 minutes before serving. Serve with additional sauce on the side. Enjoy!