Place potatoes into a pot and cover with salted water; bring to a boil. Reduce heat to medium-low and simmer until tender, about 20 minutes. Drain.
Heat oil in a skillet over medium heat. Saute chicken in hot oil until no longer pink in the center, 5 to 7 minutes. Stir onions and garlic into chicken and cook and stir until onion is translucent, about 5 minutes.
Place butternut squash in a microwave-safe dish and cover dish with plastic wrap. Cook squash in the microwave on high until squash is tender, about 10 minutes. Remove flesh from squash skin with a fork.
Puree 1 can cannellini beans with liquid in a blender until smooth.
Combine potatoes, chicken mixture, butternut squash, pureed cannellini beans, chicken broth, drained cannellini beans, butternut squash soup, celery, apples, and chili seasoning mix together in a large pot. Bring to a boil, reduce heat to medium-low, and cook until flavors blend, about 30 minutes.