Wash the chicken and pat dry. Dredge the chicken in flour to coat. In a deep skillet or Dutch oven, heat the oil and fry the chicken on both sides until they are golden-brown. Discard most of the oil, leaving the brown bits in the bottom of the pan, if possible. Add the Marsala and butter, and simmer on low heat until the wine begins to evaporate (about 2-3 minutes). Add the tomato sauce, mushrooms, onion, garlic, green onions, parsley, oregano, and basil. Cover and gently simmer for 15-20 minutes, until tender. Add the salt and pepper to taste. Serve over pasta or polenta.