Layer chicken, great Northern beans, and corn into a slow cooker.
Mix chicken broth, chicken soup, green chile peppers, and taco seasoning together in a bowl; pour over chicken mixture.
Cover and cook on Low until chicken is no longer pink in the center, 8 to 10 hours. Stir in sour cream and pepper Jack cheese; cover and cook until cheese is melted, 3 to 5 minutes.