Whisk flour, garlic salt, pepper, and oregano together in a bowl. Dredge chicken in flour mixture until lightly coated.
Heat oil and butter in a large skillet over medium heat. Add chicken and cook until lightly browned, about 2 minutes. Flip chicken and add mushrooms. Cook, stirring mushrooms occasionally, until chicken is browned on the other side, about 2 more minutes.
Pour Marsala wine over chicken. Reduce the heat to low, cover, and simmer until chicken is no longer pink in the center and the juices run clear, about 10 minutes. An instant-read thermometer inserted into the center should read at least 165 degrees F (74 degrees C).
