On a 6-inch square of foil, place wood chips or pellets. Top with another 6-inch square of foil, and crimp edges to seal. Poke several holes through top piece of foil.
In a small bowl, combine brown sugar, lemon butter garlic seasoning, paprika, and oil.
Gently loosen skin from chicken, keeping skin intact. Rub sugar mixture under skin and over chicken. Place soda cans inside chickens so cans stand straight up.
Place foil packet on one side of grill. Add chicken, standing up, to grill. Grill, covered with grill lid, until an instant-read thermometer inserted in thickest portion of breast and thigh registers 165°, about 3 hours. (Check grill periodically to make sure the temperature stays between 275° and 300°.) Remove chicken from grill, and let stand for 15 minutes before serving. Discard soda. Cut chickens in half lengthwise, removing backbone. Serve with White Barbecue Sauce, and garnish with smoked green onion, if desired.
Recipe by Taste of the South at https://tasteofthesouthmagazine.com/smoked-chicken-with-white-barbecue-sauce/