Remove and discard excess fat from chicken. Rinse and pat dry. Remove skin, if desired. Sprinkle with salt and pepper to taste. Arrange chicken, bone side down in center of cooking grate. Cover grill. Cook until meat near bone registers 165 degrees and is no longer pink and the juices run clear. Turn once during cooking.
If preparing barbecued chicken, season with favorite barbecue rub and brush sauce on chicken during the last 15 minutes of cooking time to prevent burning.