Place the thighs and drumsticks in a large Ziploc bag. In a medium bowl mix all of the ingredients for the marinade. Pour into the bag with the chicken. Set the bag of chicken in a container where the bag can lay flat and place in the refrigerator. Let it marinate for about 8 hours; turning the bag every once in a while.

Heat the broiler and place the oven rack in about the middle of the oven, so the chicken doesn't brown too quickly.

Remove the chicken from the marinade and place on a broiler pan that has been sprayed with a nonstick cooking spray. Place under the broiler and turn about every 15 minutes; basting with the marinade. Broil until the chicken is tender and juices run clear.