Place chicken between 2 pieces of plastic wrap and pound to 1/4 inch thick. Combine flour, salt, pepper and oregano and mix well. Heat the oil and butter in a skillet over medium to high heat. Dredge chicken in flour mixture.
Place chicken in skillet until brown on one side (about 2 minutes) turn over and add mushrooms around the chicken in skillet. Cook until chicken is cooked through about 3 to 5 minutes. Stir the mushrooms and and wine. Cover and simmer for 10 minutes.