Prepare the slow cooker: Place the chicken breasts at the bottom of the slow cooker.
- Add vegetables and spices: Layer the beans, corn, green chiles, onion, garlic, chili powder, cumin, oregano, garlic powder, salt, and pepper over the chicken.
- Add broth: Pour the chicken broth over the ingredients in the slow cooker.
- Cook: Cover and cook on LOW for 6–8 hours or on HIGH for 3–4 hours, until the chicken is fully cooked and tender.
- Shred the chicken: Remove the chicken breasts, shred them using two forks, and return the shredded chicken to the slow cooker.
- Add dairy: Stir in the sour cream and chopped cilantro.
- Final cook: Cover and cook on HIGH for an additional 15 minutes to heat through.
- Serve: Ladle the chili into bowls and garnish with your choice of toppings.