Place chicken into a 6-qt slow cooker. Stir in onion, bell pepper, garlic, chicken stock, tomato puree, black beans, diced tomatoes, corn, green chiles, chipotle pepper, chili powder, oregano, cumin, 3/4 teaspoon salt and 1/2 teaspoon pepper.
Cover and cook on low heat for 7-8 hours. Remove chicken and let cool before dicing into bite-size pieces, discarding bones.
Stir in chicken, lime juice and cilantro into the slow cooker; season with salt and pepper, to taste.