Between pieces of plastic wrap or waxed paper, place each chicken breast smooth side down; gently pound with flat side of meat mallet or rolling pin until 1/4 inch thick. In shallow dish, mix flour, salt and pepper.
In 12-inch nonstick skillet, heat oil over medium-high heat. Coat both sides of chicken with flour mixture. Cook chicken in hot oil 6 to 8 minutes, turning once, until chicken is no longer pink in center. Remove chicken to serving plate; cover to keep warm.
Stir broth into skillet. Heat to boiling over medium-high heat. Stir in mustard and mushrooms. Cook 2 to 3 minutes, stirring frequently, until slightly thickened. Spoon sauce over chicken. Sprinkle with thyme.