Place chicken in large resealable plastic bag or glass dish. Add 1/4 cup of the marinade; turn to coat well. Refrigerate 30 minutes or longer for extra flavor. Remove chicken from marinade. Discard any remaining marinade.
Meanwhile, cook pasta as directed on package. Rinse under cold water; drain well. Set aside. Grill chicken over medium heat 6 to 8 minutes per side or until cooked through, brushing with fresh marinade, if desired. Cut chicken into bite-size cubes.
Mix remaining 3/4 cup marinade, oil and vinegar in large bowl. Add pasta, chicken, vegetables and mozzarella cheese. Gently toss to coat well. Sprinkle with Parmesan cheese, if desired. Serve immediately or refrigerate until ready to serve. Toss lightly before serving.