Combine oil, salt, and pepper to make a paste. Rub over outside of turkey. Tie legs together with kitchen twine.
Place about 50 coals in a chimney starter, and ignite; heat until just gray. Place a 9-by-13-inch disposable aluminum roasting pan in the center of the bottom rack. Pour coals onto rack on either side of pan, dividing them evenly. Replace top grill rack. Place turkey on center of rack over pan, and cover. Grill, adding 8 coals to each pile every 45 minutes to maintain heat, until a meat thermometer inserted into the thickest part of the thigh (avoiding bone) registers 165 degrees (begin checking after about 3 hours; cooking may take up to 5 hours depending on the exact size of bird). Tent with parchment-lined foil. Let stand 30 minutes. Reserve drippings from roasting pan for Giblet Gravy.