For gas grill, ignite one side only. Grill temperature should be medium to low. Combine seasoning rub ingredients and rub on chicken inside and out as well as under the skin, if desired. Place chicken on one side of prepared grill, opposite the coals or heat source. Close grill lid and cook slowly for 1 to 2 hours or until temperature on meat thermometer is 180 F and juices run clear when thighs are pierced with fork.
Time can vary depending on intensity of grill heat.
Smokers may take up to 3 hours. It's easy to cook several chickens at a time for later use. Cooking time may need to be extended. Wrap cooled, cooked chicken in freezer foil and freeze. Reheat in conventional oven, directly from freezer.