Pound chicken breasts to 1/4 inch thick, season with salt and pepper, dredge in flour. Saute chicken in butter/oil over med-high heat for 3 minutes each side until golden, turning once. Remove the chicken to a large platter, keep warm
Lower heat to medium. Sauté mushrooms until they are browned; about 5 minutes; season with salt and pepper. Turn heat to high, add the Marsala and boil, scraping brown bits from bottom of pan. Add the chicken broth and simmer until reduced by half. Return the chicken to the pan and gently stir allowing to simmer for about 1 minute more to heat the chicken. Garnish with chopped parsley and serve.