Cook the bacon over medium heat in olive oil in a large Dutch oven until crisp, about 8 minutes. Remove with a slotted spoon and set aside. Season the chicken pieces generously with the salt and pepper and brown the pieces in 2 batches in the bacon drippings. Set aside. Pour off about half of the pan drippings then add the onions, garlic, and mushrooms. Cook over medium-high heat until browned, about 8 minutes. Stir in the potatoes and carrots. Add the 1 1/2 teaspoons salt and the flour, stir to coat the vegetables.
Pour in the wine and chicken broth, stir until you don't see any lumps of flour. Add the chicken, thyme, bay leaves, and half of the bacon to the stew. Bring to a boil then reduce to a simmer. Cover and braise until the chicken and vegetables are almost tender, about 40 minutes. Uncover and cook until sauce thickens, about 10 more minutes.
Stir in the parsley and vinegar. Adjust seasoning with salt and pepper, to taste, and serve with the remaining bacon.
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