Combine oil, butter, onion, garlic, annatto, cumin, lemon and orange juices in a large shallow pyrex pan. Add chicken halves, turning well to coat.
Cover and marinate for several hours, or overnight.
Remove the chicken from the marinade, then cook over medium coals on barbeque grill or in a broiler 4" from the source of heat.Turn frequently and cook, turning and basting frequently, for about 25 minutes or until browned on both sides.
Cut chicken halves into serving pieces. Serve with beans and rice, corn or flour tortillas and fresh salsa.