Combine all ingredients for the dry rub and divide evenly in two separate bowls. Set one bowl aside. Prepare the chicken by blotting dry with paper towels. Rub one bowl of seasoning under the skin and all over chicken pieces. Cover and refrigerate seasoned chicken pieces for at least 30 minutes or up to an hour.

Preheat your grill and scrape clean. When the grill has reached a temperature of about 325 degrees,  oil the grate with a paper towel dipped in vegetable oil gripped with tongs.

Place the chicken skin side down and grill over indirect heat (switch the burners off under the chicken if using gas) until the skin is crisp and well browned, turning occasionally. This should take about 15 to 20 minutes.

Dredge the skin side of the chicken pieces in the second bowl of seasoning and return to the grill, skin side up. Grill, covered, until the internal temperature has reached 160 degrees for white meat, and 165 for dark, about 5 to 10 minutes more. The rub should melt and turn into a deeply colored glaze on the chicken. Remove, tent with foil for about 5 minutes, and serve.