Preheat oven to 350° F.
In a large cast iron Dutch oven, cook the bacon over medium heat until browned, about 8 minutes. Use a slotted spoon to remove the bacon to a paper towel-lined plate. Reserve the drippings in the pot.
Pat the chicken dry with paper towels and season with salt and pepper. Working in batches, brown the chicken, skin-side down, until golden brown, about 5-7 minutes. Remove to a plate and set aside.
Leave 2 tablespoons of drippings in the pot, then discard any extra fat. Add onion, carrots, celery, and mushrooms and cook until the onion is translucent, about 5-7 minutes. Add the garlic and cook, stirring constantly, for 1 more minute. Pour in the wine and deglaze the pan by scraping up any browned bits from the bottom with a wooden spoon. Add the stock, thyme, bay leaf, and salt and pepper to taste.
Return the bacon and chicken (skin-side up) to the pot. Cover with a tight-fitting lid and transfer the pot to the oven. Cook at 350° F for about 40 – 50 minutes, or until the chicken is no longer pink.
Place the pot on the stovetop over medium-high heat. Bring the liquid to a simmer and cook, uncovered, until the liquid is reduced by about half, approximately 10-15 minutes. Remove from the heat; stir in the butter and vinegar. Taste and season with additional salt and pepper, if necessary. Remove bay leaf and thyme stems. Serve in individual bowls; garnish with fresh parsley.