In a small skillet, melt 1/2 cup butter. Mix in 1 tablespoon garlic salt, 1 tablespoon paprika, salt, and pepper.
Discard 1/2 the beer, leaving the remainder in the can. Add remaining butter, garlic salt, paprika, and desired amount of salt and pepper to beer can. Place can on a disposable baking sheet. Set chicken on can, inserting can into the cavity of the chicken. Baste chicken with the melted, seasoned butter.
Place baking sheet with beer and chicken on the prepared grill. Cook over low heat for about 3 hours, or until internal temperature of chicken reaches 180 degrees F