In a plastic bag combine the 1/4 cup flour, salt, pepper, and paprika. Add 2 or 3 pieces of chicken to the bag at at time. Seal; shake to coat well.
In a very large skillet heat the oil over medium heat. Cook chicken in hot oil about 10 minutes or until well browned, turning to brown evenly. Remove chicken from skillet, reserving drippings in the skillet.
Add onion, mushrooms, sweet pepper, and garlic to skillet. Cook and stir for 2 minutes. Add red wine or beef broth and balsamic vinegar. Cook and stir 5 minutes more.
Add undrained tomatoes and Italian seasoning. Bring to boiling, scraping up browned bits from the bottom of the skillet. Return chicken to the skillet; reduce heat. Cover and simmer about 20 minutes or until chicken is tender and no longer pink. Remove chicken; keep warm.
Stir together half-and-half or light cream and the 1 tablespoon flour; add to skillet. Cook and stir until slightly thickened and bubbly. Cook and stir 1 minute more. Return chicken to pan; heat through. Sprinkle with parsley. Serve over hot cooked pasta, if desired.