1. Lay chicken pieces skin-side up in baking pan. Peel and slice carrots on the bias (diagonal cut) and add to pan.
2. Wash oranges well. Using a microplane or fine grater, zest one orange into a small bowl. Slice zested orange in half and squeeze the juice into the bowl. Slice remaining three oranges into eighths and set aside for later use.
3. Add remaining ingredients and mix until thoroughly incorporated. Pour glaze over chicken, and allow to marinate for up to 24 hours.
4. Bake covered at 350°F (180°C) for one hour. Add eight orange slices, baste with pan juices, and bake another 30 minutes or until chicken is crisp.
5. You can discard the cooked orange slices and replace with fresh slices for serving, if desired.