Heat 2 tablespoons olive oil in a Dutch oven or similar deep, sturdy pot over medium-high. Season both sides of the chicken with salt and pepper.

Once the oil is hot and shimmering (but not so hot it starts smoking), add the chicken in a single layer. Cook on the first side for 3 to 4 minutes, until browned, moving the chicken as little as possible so that it gets a nice sear. Flip and brown on the other side, about 2 additional minutes. Transfer the chicken to a large, clean plate. The chicken does not need to be cooked through.

Reduce the heat to medium. Add the remaining 1 tablespoon oil, onion, and peppers. Cook until the vegetables begin to soften, about 4 minutes.

Add the garlic and cook for 1 minute, or until the garlic is fragrant.

Add the white wine. Stir and let simmer until the wine is reduced by approximately half, about 3 minutes.

Add the tomatoes with their juices, mushrooms, Italian seasoning, and balsamic vinegar, stirring to combine. Bring to a simmer. Let the sauce simmer, uncovered, for 10 minutes.

Nestle the chicken thighs into the tomato sauce, along with any drippings that have collected on the plate. The chicken should be mostly submerged, though some may peek through.

Cover the pot and let simmer 30-45 additional minutes, or until the chicken is cooked through, the sauce is thickened, and the mushrooms are tender.

If you’d like to dice or shred the chicken, remove it to a cutting board. When cool enough to handle, dice or shred it, then return it to the pot. You also can serve the chicken thighs whole.

Taste and season the sauce with additional salt and pepper as desired.

Serve hot over pasta, rice, polenta, or veggie noodles if desired - serve with a big extra spoonful of sauce and a sprinkle of basil or parsley and Parmesan.