To make the marinade, in a small bowl, stir together the oil, orange juice, rosemary, garlic, and salt and pepper to taste. Pour the marinade into a large, strong lock-top plastic bag. Add the chicken and seal the bag. Turn the bag to coat the chicken with the marinade. Place in the refrigerator and marinate for 8-24 hours, turning the bag occasionally to coat the chicken evenly. Drain the marinade from the chicken, reserving the marinade.

Heat a covered grill (barbecue) to medium-hot. Place the chicken on the grill rack, skin side up. Brush with some of the reserved marinade. Cover and cook for 30 minutes. Brush with additional marinade. Cover and cook until the chicken is no longer pink, 30-40 minutes more. Discard any remaining marinade. Or, if you don’t have a covered grill, cook on an open grill over medium-hot coals, but baste with the marinade about every 10 minutes to prevent the meat from drying out.

Transfer the chicken to a platter and serve all at once.