In a small bowl, combine the first seven ingredients. Pour 1-1/2 cups marinade into a large resealable plastic bag; add the chicken. Seal bag and turn to coat; refrigerate overnight. Cover and refrigerate remaining marinade.
Drain and discard marinade. Add barbecue sauce to reserved marinade. Using long-handled tongs, moisten a paper towel with cooking oil and lightly coat the grill rack.
Prepare grill for indirect heat using a drip pan. Place chicken over drip pan and grill, covered, over indirect medium heat for 35-50 minutes or until a meat thermometer reads 170°, turning and basting occasionally with marinade. Before serving, brush with remaining marinade. Yield: 8 servings.