Heat 1 tablespoon oil in a large pan or skillet over medium heat and fry prosciutto until crisp. Add chicken fillets and sear on both sides. Remove chicken and prosciutto from skillet and set aside.
Heat 2 tablespoons oil to the same pan or skillet and add mushrooms, onion and red pepper. Cook until onion is tender. Add oregano, salt and pepper and cook for ½ minute. Add wine and deglaze scraping bits from the bottom of the pan. Cook over low heat until wine has evaporated. Stir in chopped tomatoes and bring to a boil. Return chicken fillets and prosciutto to the pan or skillet, cover pan and cook for 10 minutes more over low heat or until chicken is tender.
Stir in parsley and correct seasoning.
Serve with Parmesan polenta.