1. Preheat oven to 350 degrees Fahrenheit.
2. Run your fingers under the skin of each chicken quarter to separate it from the meat. Place about one to two tablespoons of veggie puree under the skin of each, gently pressing to evenly distribute. (You will have extra puree.)
3. Slice onion and fennel into rounds and lay in an even layer on a roasting pan. Place the stuffed chicken above them and drizzle with the olive oil. Squeeze the juice and zest the peel of the orange, then sprinkle with thyme. Season with salt and pepper.
4. Bake one hour covered, then uncovered for half an hour, until tender and juices run clear. Transfer the chicken to a platter.
5. Stir the orange juice, thyme, onion, and fennel. Scrape up any browned bits from the bottom, spoon the sauce over the chicken, and serve.