Add the barbecue sauce to the half-full can of beer.
In a small bowl, combine the basil, paprika, onion powder, garlic powder, salt and pepper; mix well and rub evenly over the chicken.
Place the cavity of the chicken over the beer can so that the chicken is sitting on the can, then place on the rack in the center of the grill.
Cover the grill and cook for 1 to 1 1/4 hours, or until no pink remains and the juices run clear.
Carefully pour the remaining sauce from the can into a bowl, and serve with the chicken.
This can also be made with nonalcoholic beer or, for a different flavor, you could use a half-filled can of lemonade and rub the chicken with lemon-pepper seasoning. Cooking time will vary depending on the grill used.