Place a deep, ovenproof sauté pan over medium-high heat. Add oil and butter. When foam subsides, add chicken pieces, skin side down. Brown well, adjusting heat as needed, then turn and cook for 3 minutes. Add thyme sprigs and transfer pan to oven. Roast chicken, basting every few minutes.
04When chicken is cooked (20 to 30 minutes), transfer it to a platter and keep warm. Place pan back on stove, over medium heat. Add shallot and sauté one minute. Pour in sherry and boil, scraping up any pan drippings. Reduce until pan is almost dry, then add tomatoes and increase heat to high. Cook until tomatoes have broken down and juices have condensed, 10 minutes. It should be pulpy, not drippy. Taste and adjust seasoning, sprinkle with vinegar, then spoon sauce over chicken. Serve.