Combine flour, oregano, salt and pepper in a medium sized bowl.

Coat chicken breasts in flour mixture.

Heat butter and oil over medium heat in a medium sized skillet that has a lid available.

Carefully place the chicken breasts in the pan and move them around a bit so they don't immediately stick to the pan. Cook for 6 to 8 minutes, and then carefully flip the breasts over in the pan. Again move the breasts around a little, and cook for 2 - 3 minutes.

Add the mushrooms, marsala wine and sherry to the pan. Let it simmer hot for a minute and shake the ingredients together a bit. Then cover the pan, reduce the heat to medium-low and allow it to simmer and thicken for another 8 to 10 minutes.