In a large bowl, thoroughly stir together the marinade ingredients. Reserve about 1/4 cup in a small bowl to brush on chicken while grilling.
Add the chicken to the marinade, turning in order to coat. Cover and refrigerate for at least 2 hours, turning occasionally.
Preheat the grill on high, and lightly spray the grill rack with vegetable oil spray.
Grill the chicken for 30 to 45 minutes, or until the chicken is no longer pink in the center. While cooking, brush the pieces with reserved marinade and turn them frequently. Remove from heat and serve.
Preheat the broiler and lightly spray a broiler safe baking sheet with vegetable oil spray.
Put the chicken on the prepared sheet and broil about 5 inches from the heat for 25 to 30 minutes, or until the chicken is no longer pink in the center. While cooking brush the pieces with marinade and turn them frequently. Remove from heat and serve.