Preheat your oven to 350°F (175°C).
Season the chicken thighs with salt and pepper. In a large oven-proof skillet or Dutch oven, heat the olive oil over medium-high heat. Add the chicken and sear until golden brown, about 4 minutes per side. Remove the chicken and set aside.
In the same pan, add the onions and sauté until translucent, about 3 minutes. Add the garlic, and cook for an additional minute until fragrant.
Stir in the mushrooms, carrots, and celery, and cook for 5 minutes, or until the vegetables begin to soften.
Deglaze the pan with the red wine, scraping any browned bits from the bottom of the pan.
Add the crushed tomatoes, chicken broth, balsamic vinegar, Italian seasoning, and bay leaves. Bring to a simmer.
Place the chicken thighs back into the pan, nestling them into the sauce. Cover with a lid or aluminum foil and transfer to the preheated oven.
Bake for 45 minutes. Then, uncover and bake for an additional 15 minutes to allow the sauce to thicken slightly.
Remove from the oven, discard the bay leaves, and garnish with fresh basil.
Serve the Bolognese Chicken Cacciatore with a side of pasta, rice, or crusty bread to soak up the delicious sauce.