Between sheets of plastic wrap or waxed paper, flatten each chicken breast half to 1/4-inch thickness. In shallow dish, mix bread crumbs and Parmesan cheese. In another shallow dish, beat egg. Dip chicken into egg, then coat with bread crumb mixture.
In 12-inch skillet, heat oil over medium heat. Cook chicken in oil 10 to 15 minutes, turning once, until no longer pink in center. Pour pasta sauce around chicken in skillet; heat until hot. Sprinkle mozzarella cheese over chicken.