Preheat 450. Combine tomatoes, 2 T oil, herbes de provence in a large bowl. Season with salt and pepper. Heat 1 T oil in large heavy ovenproof skillet until oil shimmers. Carefully add tomatoes to pan. Transfer skillet to oven and roast, turning once, until tomatoes burst, about 15 minutes. Transfer to medium bowl and drizzle with worcestershire sauce.
Meanwhile, season chicken with 1 tsp salt and pepper. Heat 2 T oil in large oven proof skillet over medium heat. Sear chicken on both sides until golden brown, 6-8 minutes. Transfer pan to oven adn roast until cooked through, 8-10 minutes. Transfer chicken to cutting board and let rest for at least 5 minutes.
Add remaining T of oil to same skillet, heat over medium heat. Add shallot of cook, stirring often, until fragrant, about 1 minute. Deglaze pan with vinegar, scraping up brown bits. Add tomatoes and juices and siommer until sauce is beginning to thicken, about 1 minute. Season as needed with salt and pepper.
Slice chicken, divide amongst plates. Sppon tomatoes and sauce over meat.
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