For the chicken: Preheat the oven to 400 degrees F. Wash the chicken well and blot dry on paper towels. Transfer to a large roasting pan or baking sheet and drizzle with some oil. Sprinkle generously with salt and pepper and toss well. Arrange the chicken pieces skin-side-up in a single layer. Roast until golden brown, about 30 minutes.
For the sauce: Meanwhile, place the onion, garlic, hot peppers if using and the oil in a pot over medium-high heat and cook until slightly softened, about 5 minutes. Add the bell peppers and cook 2 to 3 more minutes. Add the mushrooms and olives and season with salt and pepper, keeping in mind that the olives are salty. Crush the tomatoes with your hands until coarse and add to the pot, stirring well. Bring the sauce to a simmer and taste for seasoning. Let simmer 20 minutes, and then stir in the parsley.
Remove the chicken from the oven and pour the sauce over the chicken, covering completely. Return to the oven and bake 30 to 40 minutes. Serve while hot, with rice or polenta if desired.