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Preheat the oven to 450 degrees. Set a large ovenproof skillet over medium-high heat. Add oil; when it is hot, place chicken in the skillet, skin side down. Cook undisturbed for about 5 minutes, or until chicken is nicely browned. Turn and cook 3 minutes on the other side. Season with salt and pepper.
Place skillet in the oven. Cook 15 to 20 minutes, or until almost done (juices will run clear, and there will be just a trace of pink near the bone). Remove chicken to an ovenproof platter. Place it in the oven; turn off the heat, and leave the door slightly ajar.
Pour all but 2 tablespoons of the cooking juices out of the skillet (discard them). Place skillet over medium-high heat, and add shallots; sprinkle them with a little salt and pepper, and cook, stirring, until tender, about 2 minutes. Add vinegar, and raise the heat to high. Cook a minute or two, or until the powerful acrid smell has subsided somewhat. Add 1/2 cup water, and cook for another 2 minutes, stirring, until the mixture is slightly reduced and somewhat thickened. Stir in butter, if desired.
Return the chicken and any accumulated juices to the skillet, and turn the chicken in the sauce. Serve immediately.