Sprinkle the chicken pieces with 1 teaspoon of each salt and pepper. Dredge the chicken pieces in the flour to coat lightly.
In a large heavy saute pan, heat the oil over a medium-high heat. Add the chicken pieces to the pan and saute just until brown, about 5 minutes per side. If all the chicken does not fit in the pan, saute it in 2 batches. Transfer the chicken to a plate and set aside.
Add the bell pepper, onion, carrot, mushrooms, and garlic to the same pan and saute over medium heat until they are tender and slightly browned, about 10 minutes, stirring only occasionally.
Add the wine and simmer until reduced by half, about 3 minutes. Add entire can of tomatoes with the juice (crushing them with your hands), broth, capers and Italian seasoning. Sir to combine. Return the chicken pieces to the pan and turn them to coat in the sauce. Bring the sauce to a simmer. Continue simmering over medium-low heat until the chicken is just cooked through, for about 20 minutes.
Serve chicken with additional sauce over polenta, pasta, or potatoes.
Notes
I prefer to trim any excess fat and skin off of the chicken thighs. This step is not necessary but is my personal preference.
You can make the prep work easier by pulsing the vegetables in the food processor as opposed to chopping them by hand.
Choose a dry red wine and not something sweet.
As with any recipe, add salt and pepper prior to serving according to taste, if needed. With all of the tomatoes, additional salt might be needed to balance everything out.