Cut chicken into 10 pieces: 2 legs, 2 thighs, 2 wings, and a quartered breast. In a large heavy pot or Dutch oven heat a 3-count of olive oil (about 3 tablespoons) over medium heat. Season flour with salt and pepper. Dredge chicken pieces in flour mixture a few pieces at a time. Cook for 7 to 10 minutes, browning all over. Add carrots, onion, celery, thyme, and bay leaf. Pour in wine and deglaze the pan, using a wooden spoon to scrape up any brown bits from the bottom of the pan. Cover and simmer over low heat for 1 hour. Remove lid and transfer chicken to a clean platter. Strain the braising liquid and discard the vegetables. Simmer the liquid about 15 minutes until reduced, syrupy, and slightly glossy. Place chicken back in the liquid.

In a large saute pan cook bacon over medium heat to render the fat. Once bacon is crispy, remove from pan and drain on paper towels, reserving the fat in the pan. Add pearl onions to the pan and saute until golden and caramelized; season with salt and pepper and set aside. Cook the mushrooms in the same pan; season well with salt and pepper. Toss bacon, onions, and mushrooms back into the pot with the chicken. Sprinkle with chopped parsley and serve.