Place 1 chicken breast half, boned side up, between 2 pieces of plastic wrap or waxed paper. Working from center, gently pound chicken with flat side of meat mallet or rolling pin until about 1/4 inch thick; remove wrap. Repeat with remaining chicken breast halves.
In medium bowl, combine bread crumbs, Parmesan cheese and parsley; mix well. Dip chicken in beaten egg; coat with bread crumb mixture.
In large nonstick skillet, heat oil over medium-high heat until hot. Add chicken; cook 8 to 10 minutes or until chicken is fork-tender and juices run clear, turning once.
Meanwhile, heat spaghetti sauce. Sprinkle chicken with mozzarella cheese; cover skillet to melt cheese. Serve sauce with chicken.