Cook bacon in a wide heavy pot over medium heat for 5 to 6 minutes until browned. Transfer to a bowl and cook mushrooms in the drippings for 5 minutes; add them to the bacon bowl.
Pat chicken dry and season with salt and pepper. Brown in two batches in the same pot, skin-side down for 6 minutes and on the second side for 2 minutes; transfer to a plate and leave about 1 tablespoon fat in the pot.
Cook pearl onions and carrots for 4 minutes, add garlic for 30 seconds, then stir in flour for 1 minute. Pour in wine and broth gradually, scraping up browned bits, and add thyme and bay leaf.
Return chicken skin-side up with its juices, bring to a gentle simmer and cover. Cook over low heat for 30 to 35 minutes until tender and the thickest meat reaches 175 to 185°F.
Return bacon and mushrooms and simmer uncovered for 5 minutes. Remove thyme stems and bay leaf, then lift the chicken to a platter and spoon the wine sauce and vegetables around it.