If using hickory, at least 1 hour before grilling, soak chips in enough water to cover. Cut chicken into quarters or eight pieces, if you like. Place in a plastic bag in a shallow dish.
In a medium bowl, stir together vinegar, Worcestershire sauce, brown sugar, liquid smoke, seasoned salt, and pepper. Pour the mixture over chicken in plastic bag. Close the bag. Marinate the chicken in the refrigerator for 2 to 4 hours, turning the bag occasionally.
Drain chicken, reserving the marinade. In a covered grill, arrange preheated coals around a drip pan for indirect grilling. Test for medium* heat above pan. Place chicken, bone side down, on grill rack over drip pan. Add some hickory chips for additional smoke flavor, if you like.
Cover and grill 50 to 60 minutes or until chicken is tender and no longer pink, turning once and brushing once with the reserved marinade halfway through the grilling time. Discard any remaining marinade. Makes 4 servings.
To test the temperature of the preheated coals, place your hand above the coals at the height the food will be cooked. Start counting and if you need to remove your hand after 4 seconds, the coals are medium.