Salt and pepper the chicken and then toss it in the flour to lightly coat it.
Heat olive oil in your dutch oven and, working in batches, brown chicken over medium high heat, about 3 minutes per side.
Remove the chicken from the pot and set aside on a plate.
Add peppers, onions, mushrooms, garlic, and 1/2 tsp salt to the pot and cook for 2-3 minutes.
Add wine and bring to a simmer, cooking until the liquid is reduced by half.
Add tomatoes, broth, and 1 tsp of salt to the pot.
Place chicken into the post nestling them into the sauce.
Bring the sauce to a simmer and put the lid on.
Cook for 20 - 30 minutes, until chicken is cooked through and tender.
Serve over pasta, rice, or with a thick, crusty bread.