Melt butter in a heavy saucepan. Add next 7 ingredients; bring to a boil, stirring vigorously. Pour sauce over chicken; cover, and marinate at least 4 hours in refrigerator.
Place chicken, skin side down, on grill over medium coals; reserve sauce. Grill 12 minutes; turn skin side up, and cook 12 minutes. Brush chicken with reserved sauce; grill an additional 40 minutes, basting and turning every 10 minutes.