Remove and discard giblets and neck from chicken. Rinse chicken with cold water; pat dry. Trim excess fat. Place chicken, breast side down, on a cutting surface. Cut chicken in half lengthwise along backbone, cutting to, but not through, other side. Turn chicken over. Starting at the neck cavity, loosen skin from breast and drumsticks by inserting fingers, gently pushing between skin and meat. Place chicken, breast side up, in a large shallow dish. Combine buttermilk and remaining ingredients except cooking spray; pour under skin and over surface of chicken. Cut a 1-inch slit in skin at the bottom of each breast half. Insert tip of each drumstick into each slit. Cover and marinate in refrigerator 24 hours.
To prepare chicken for indirect grilling, preheat grill to medium-hot using both burners. After preheating, turn left burner off (leave right burner on). Place a disposable aluminum foil pan on briquettes on left side. Pour 2 cups water in pan. Coat grill rack with cooking spray; place on grill. Place chicken, skin side down, on grill rack covering left burner. Cover and grill 1 1/2 hours or until a meat thermometer registers 180°, turning halfway during cooking time. Discard skin before serving.