Gently flatten the chicken breasts by pounding each one between sheets of plastic wrap or in a food storage bag. They should be fairly uniform in thickness so they will cook evenly.

Melt the butter and olive oil in a large skillet over medium-high heat.

In a shallow bowl, combine the flour, salt, and pepper; blend thoroughly with a fork. Dip the chicken pieces in the flour mixture to coat.

Arrange the chicken pieces in the hot fat and brown for about 2 to 3 minutes on each side. Remove the chicken pieces to a plate and set aside.

Add the mushrooms to the skillet and cook them for about 2 minutes.

Add the chicken pieces back to the pan along with the marsala wine. Reduce the heat to medium-low and cover the pan. Simmer for 10 minutes, or until the chicken is thoroughly cooked. The minimum safe temperature for chicken is 165 F.

Garnish with parsley or green onion tops, if desired

Serve the chicken over hot cooked rice, spaghetti or capellini, or potatoes.