How to Make It
In a large heavy nonreactive skillet, heat the oil. Season the chicken thighs with salt and pepper. Add them to the skillet skin side down and cook over moderately high heat, turning once, until browned, about 15 minutes; transfer to a plate.
Add the carrot, celery and onion to the skillet and cook over moderate heat, stirring, until barely soft, about 3 minutes. Add the vinegar and wine and boil until nearly evaporated, scraping up the browned bits from the bottom of the skillet, about 1 minute. Return the chicken to the skillet and add the stock, thyme, bay leaves and allspice. Cover tightly and simmer gently over low heat until tender, about 30 minutes. Transfer the chicken and vegetables to a platter, cover and keep warm. Discard the bay leaves.
Skim the fat from the liquid in the skillet, then boil the juices until reduced to 1/2 cup. Remove the skillet from the heat and swirl in the butter until blended. Add the parsley and season with salt and pepper. Pour the sauce over the chicken and serve.