Preheat the oven to 400 degrees. On a large rimmed baking sheet, rub the bell peppers with 1 tablespoon of the olive oil. Roast the peppers for about 45 minutes, turning them halfway through, until the skins are blistered. When cool enough to handle, peel the bell peppers and slice them into 1/2-inch-wide strips. Lower the oven temperature to 350 degrees.

Meanwhile, season the chicken pieces with salt and pepper. In a very large skillet, heat 3 tablespoons of the olive oil until shimmering. Working in 2 batches, cook the chicken over moderately high heat until it is golden all over, about 10 minutes per batch. Transfer the browned chicken pieces to a large roasting pan.

Add the carrots, celery, garlic, thyme, and half of the onions to the skillet and cook over moderate heat until the onion is translucent, about 5 minutes. Using a slotted spoon, transfer the vegetables to the roasting pan with the chicken. Discard the fat from the skillet.

Set the skillet over high heat. Add the white wine and bring to a boil, scraping up the browned bits from the bottom of the pan. Pour the wine over the chicken. Add the chicken stock to the roasting pan, cover with foil and transfer to the oven. Braise the chicken for about 1 1/2 hours, until it's falling off the bone.

Transfer the chicken to a serving dish and cover with foil. Set the roasting pan over high heat and boil the juices for 15 minutes. Season the sauce with salt and pepper.

Meanwhile, in a large skillet, heat the remaining 2 tablespoons of oil. Add the remaining onion and cook over moderate heat until tender, 8 minutes. Stir the onion, peppers, and olives into the sauce and simmer until heated through, about 1 minute. Pour the sauce and vegetables over the chicken, sprinkle with parsley and serve with crusty bread.