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1. Heat a large covered ovenproof saute pan or Dutch oven over medium heat, and lightly coat the pan with oil. Brown the chicken in batches (to prevent crowding) until each piece is golden brown and the skin is crispy. Set aside on a platter.
2. Drain most of the fat from the pan, leaving a small amount in the bottom. Add the mushrooms and saute until golden brown and crispy, about 3 minutes. Add the onions and fennel, and saute until golden brown and quite limp, about 15 minutes. Add the garlic, the tomatoes and their juices, the wine, the stock, and bay leaf. Reduce the heat and simmer the mixture until it reduces and has thickened, about 30 minutes.
3. While the sauce is cooking, preheat the oven to 325 degrees.
4. Season the sauce with salt and pepper. Add the chicken and any collected juices back to the pan. Cover the pan and place it in the oven. Braise the chicken until it is cooked through and the juices run clear when a thigh is pricked, about 45 minutes.
5. Sprinkle the capers, olives, and parsley on top of the chicken.