Season the chicken with salt and pepper. Melt 2 tablespoons of the butter in a large skillet until foaming, then, a few pieces at a time, brown the chicken well on all sides. You're not cooking the chicken here; just making the skin crisp and giving it color, so 5 minutes per side is about right. Remove the chicken to a plate.
Add the garlic to the pan and cook about 10 minutes. Deglaze the pan with the vinegar and boil to reduce by half, 10 to 15 minutes. Return the chicken to the pan. Add the tomatoes and tomato paste. Using a piece of kitchen twine, tie together the thyme, parsley, and bay leaf. Add the herb bundle to the chicken and simmer, uncovered, until the meat falls from the bone, about 30 minutes. Transfer the chicken to a dish, cover, and keep warm.
Pour the stock into the pan juices and boil until thickened, about 10 minutes. Strain into a saucepan, and if it's still not concentrated enough for you liking, boil it down a little more. Whisk in the remaining tablespoon of butter. Season, and pour over the chicken. Serve with chopped parsley, sprinkled over, and with a bowl of roasted or mashed potatoes on the side.
Recipe courtesy Laura Calder, "French Food at Home", William Morrow, 2003