In a large bowl toss the tomatoes, 2 tablespoons of olive oil, herbes de Provence, and salt and pepper to taste. Place tomatoes in a rimmed baking dish and roast in oven for about 15 minutes, or until tomatoes burst and give up some of their juices. Remove from oven and drizzle with Worcestershire sauce.
Meanwhile, season chicken all over with salt and pepper. Heat 2 tablespoons of olive oil a large ovensafe skillet over medium-high heat. Sear the chicken on both sides until golden brown, about 6 to 8 minutes total. Transfer pan to the oven and roast until chicken registers 165°F with an instant-read thermometer, about 8 to 10 minutes. Transfer chicken to a cutting board and allow to rest for at least 5 minutes.
Add remaining 1 tablespoon of olive oil to the pan and heat over medium heat, being careful not to place hands on handle as the pan will still be extremely hot. Add shallot to pan and cook, stirring, until fragrant, about 1 minute. Deglaze the pan with the vinegar, scraping up any browned bits from the bottom of the pan with a wooden spoon. Add the tomatoes and their juices and simmer until a sauce begins to form, about 1 minute.
Slice chicken and divide among plates. Spoon tomatoes and sauce over and garnish with parsley.