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Step 1
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.
Step 2
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.
Step 3
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.
Step 4
Return the chicken and any accumulated juices to the skillet, and turn the chicken in the sauce. Serve immediately.