About an hour before you want to start cooking, remove the chicken breasts from the fridge and season with the rub. No binder required: Season liberally on both sides and on the edges, as best you can, covering all exposed meat to the rub. Let the seasoned meat 'setup' outside the fridge, preferably out of reach of interested and hungry golden retrievers. I like to let the meat sit on a wire cooling rack, on a cookie sheet, so the air can circulate all around it.
Preheat your smoker or grill to 400 degrees. (This will be an indirect cook. My smoker usually takes 20-30 minutes to come up to temp.)
Put the seasoned chicken breasts on the smoker, cook about 25 minutes or until internal temperature reaches 155 degrees.
For the last 5 minutes of the cook, baste both sides of each chicken breast with the Carolina BBQ sauce. You want to leave it on the smoker long enough so the sauce adheres to the meat, but not so long that it starts to burn the meat because of the sugar content.
Remove the chicken from the grill at 160 degrees internal temperature. You want internal temperature to reach 165 degrees before eating, but the temperature will continue to rise once you remove it from the grill. It's easy to overcook and dry out the breasts, so monitor the temperatures with a wireless thermometer if you can!