Flatten each chicken breast half to 1/4-inch thickness by gently pounding between sheets of plastic wrap or waxed paper. Mix four, salt and pepper. Coat chicken with flour mixture; shake off excess flour.
Heat oil in 10-inch skillet over medium-high heat. Cook garlic and parsley in oil for 5 minutes, stirring frequently.
Add chicken to skillet. Cook, turning once, until brown.
Add mushrooms and wine.
Cook 8 to 10 minutes, turning chicken once, until chicken is no longer pink in center.