In a Dutch oven or large braiser, cook the bacon until crisp. Remove from pan and set aside.
Season the chicken with salt and pepper and add it to the pan, but don’t overcrowd. Cook until chicken is well browned, in batches if necessary. Remove chicken from pan.
Add the onions, garlic, carrots, and mushrooms to the pan and cook until vegetables start to soften. Add the chicken back to the pan. Add the broth, vinegar, thyme, pearl onions, and reserved bacon. Bring to a boil, reduce to a low simmer and cover. Simmer over low heat for 50-60 minutes, until chicken is cooked through.
Mix the arrowroot with 2 tablespoons cold water and stir until smooth. Add this to the pot and bring to a boil. Simmer for 10-15 minutes, until sauce is slightly thickened before serving.