Remove neck and giblets from the turkey - reserve for other uses. Remove and discard excess fat. Rinse bird inside and out and pat dry. Season body cavity with salt and pepper. Tie legs together and twist wing tips under back. Brush turkey with oil and lightly sprinkle with salt and pepper. Arrange turkey, breast side up, on the cooking grate over indirect medium heat. Place lid on grill. Cook 11 to 13 minutes per pound or until a meat thermometer registers 180ºF. and the juices run clear. Transfer turkey to a platter and let stand 15 minutes before carving.
Gas Grill Turkey Tip: Be sure to place the turkey in a foil-drip pan when using a gas grill. About 20 minutes before the bird is done, remove the foil-drip pan and place the bird in the center of cooking grate. This allows the bottom of the bird to get some color and gives the opportunity to make a gravy from the drippings that have accumulated in the foil-drip pan. Makes 12 to 15 servings.