In small bowl, combine first six ingredients. Spread on chicken pieces and place in resealable bag or air-tight container. Refrigerate overnight.
To cook, prepare grill for direct cooking over medium heat (350°F-450°F). Place chicken skin side down and cook, covered, 10-15 minutes. Turn chicken, sprinkle cooked side with grated parmesan and grill, covered, an additional 10 minutes or longer until cooked through (165°F).