Turn the chicken frequently as it grills so the heat doesn't char the sugars in the sauce.
Not grilling weather? Broil this chicken in your oven. Set oven control to broil. Place chicken skin side down on broiler pan. Broil with top of chicken 6 inches from heat 25 to 30 minutes, turning frequently and brushing with marinade from plastic bag, until juice of chicken is clear when thickest piece is cut to bone (170°F for breasts, 180°F for thighs and drumsticks).