This braised chicken has nice saltiness from the olives that goes well with polenta, potato purée, or simply boiled potatoes. Make sure you use good-quality olives when preparing this dish.
Season the chicken with salt and pepper.
In a Dutch oven over high heat, heat the oil until very hot. Add the chicken, skin side down, and brown well on all sides, about 6 minutes total. Remove and set aside.
Lower the heat to medium, add the onion, and cook for about 5 minutes. Add the celery and cook until the vegetables are soft, about 5 minutes longer. Add the thyme, oregano, bay leaves, and crushed hot red pepper and cook for another minute or two.
Add the lemon juice and orange juice, and 1 minute later add the broth or water, tomatoes, olives, and parsley.
Partially cover the pan and let cook for 25-30 minutes or until tender. Carve the chicken if necessary and serve it garnished with more olives on top.