Place the chicken in the slow cooker. Sprinkle on the chili powder, cumin, and salt and pepper. Add the onion, bell pepper, tomatoes, chicken broth, tomato paste, chipotle, and black beans. Stir, place the lid on the slow cooker, and cook on high for 5 hours or high (or 8 hours on low.) Stir in the lime juice.
Using 2 forks, break up the chicken into chunks (or you may shred it more fine.) Taste and add more salt if the soup needs it.
Serve it piping hot in a bowl with avocado, sour cream, grated cheese, and cilantro leaves on top!