1. Rinse the chicken pieces, pat dry, and place in a bowl.
2. Combine the marinade ingredients and mix well.
3. Add the marinade to the chicken and coat the pieces evenly.
4. Cover and refrigerate for at least 30 minutes or up to 8 hours.
5. To grill: Heat grill to medium temperature and brush the cooking rack with oil, then lay the chicken skin-side up in the center of the rack.
6. Cover the grill and regulate the heat so that it remains at a medium temperature.
7. Grill the chicken for about 12 minutes on each side.
8. The chicken is done when the breasts register 160° and the thighs register 170° on a meat thermometer.
9. As the chicken cooks, brush on the remaining marinade.
10. To roast: Preheat the oven to 425°.
11. Roast the chicken until the juices run clear when the meat is prodded deeply with fork, about 30 minutes.
12. During roasting, brush with the marinades.