In a 3 1/2- or 4-quart slow cooker combine onion, carrots, celery, and garlic. Add chicken; sprinkle with salt and pepper. Combine in a medium bowl the undrained tomatoes, chicken broth, wine, and Italian seasoning. Pour over mixture in cooker.
Cover and cook on low-heat setting for 6 to 7 hours or on high-heat setting for 3 to 3 1/2 hours. Turn off cooker. Stir beans into chicken mixture in cooker. Cover and let stand for 10 minutes.
With a slotted spoon, transfer chicken and vegetables to serving bowls, reserving cooking liquid. Drizzle chicken and vegetables with enough of the liquid to moisten. Sprinkle each serving with Parmesan cheese.