Place chicken in a 3-1/2- or 4-quart slow cooker. Sprinkle lightly with salt and pepper. Pour pasta sauce over chicken.
Cover and cook on low-heat setting for 6 to 7 hours or on high-heat setting for 3 to 3-1/2 hours, adding green beans for the last 30 minutes of cooking.
Remove chicken and green beans to a serving platter. Stir cooked pasta into sauce in cooker; serve with the chicken and beans. If desired, sprinkle with Parmesan cheese. Makes 6 servings.