Loosen the chicken skin from the chicken quarters. Do this carefully and be sure not to rip the skin.
Sprinkle the spice rub or spice blend over the entire surface of the chicken quarters. Also make sure to sprinkle the blend or rub inside of the pocket you created by loosening the skin.
Massage the spice rub into the chicken quarters liberally. The reason the spice rub is called a rub is because it needs to be rubbed in.
Heat the charcoal grill to 250º-300º F.
Bank the coals to one side of the grill. This places the heat on one side so that the meat can be placed on the other.
Cook the chicken quarters on the side of the grill opposite of the side containing the heat. This will take between 2-6 hours depending on the actual heat, the thickness of the quarters, and the time of year in which you are cooking.
Check your heat every 30 minutes to make sure that you are staying within the range of 225º-275º. If the heat is too high you can sprinkle some water on the coals to cool them down; if the heat is too low you can add a few more coals.
Remove the chicken quarters when the internal temperature reads between 165º-175º. Do not remove them before they reach 165º!