Season the chicken generously with salt and pepper to taste. In a large, deep skillet (big enough to hold all chicken fairly close together; or use two skillets) melt 3 tablespoons of the butter in 1 tablespoon of the olive oil over medium high heat. Brown the chicken for about 8 minutes, turning so both sides get nicely browned. Transfer the chicken to a deep, broad, ovenproof casserole that can go from the oven to the table. Remove the skillet from the heat and pour off most of the fat.

Preheat the oven to 375°F.

Place the skillet back over medium heat and add the remaining 1 tablespoon butter and 1 tablespoon olive oil. Add the shallots and garlic and cook for about 1 minute, or until they become translucent. Add the vinegar and wine, and stir up the crispy bits that have stuck to the bottom of the pan. Allow the liquids to cook down a bit, stirring occasionally, for about 8 minutes. Whisk in the tomato paste and let the sauce simmer and condense, about 5 minutes more. Then add the chicken stock, a little at a time. Keep stirring to mix well.

Pour the sauce over the chicken. Bake for 35 to 45 minutes until the chicken is very tender, turning the chicken pieces midway through, so that both sides are infused with the sauce. Remove one thigh and cut into it to make sure it is done and no red juices flow from the cut.

Remove the casserole from the oven, sprinkle the parsley on top, and serve.