1. Heat the oil in a large covered casserole dish over medium-high heat. Add the bacon and cook, stirring, until lightly browned and fat renders, about 5 minutes. Transfer bacon to a small bowl.
2. Meanwhile, season the flour with 1/2 teaspoon salt and some pepper in a large bowl. Add the chicken and turn to coat completely.
3. Shake excess flour from chicken and brown in the casserole, about 4 minutes per side. Remove to a plate and pour off all but 2 tablespoons fat from the casserole. Add the onion and mushrooms and cook, stirring, until the onions are soft, about 3 minutes. Pour in the wine, increase the heat to high and boil, stirring to pick up any browned bits on the bottom, until reduced by half. Return the chicken to the casserole, add the thyme and reduce heat to medium. Sprinkle half of the bacon into the pot, cover and cook until the chicken is tender, about 30 minutes.
4. Remove the chicken and sauce to a serving plate or platter. Garnish with parsley and remaining bacon and serve with polenta, if desired.
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