Add chicken breast to crock pot and top with, garlic, salt, cumin, pepper, chiles, and onion. Stir to coat chicken breasts. Cover with chicken broth and cook on high for 4 hours or low for 6 hours.
About 30 minutes before the end of cooking, remove the lid of the slow cooker and shred the chicken into bite-size pieces. Now add your beans and return lid to finish cooking.
Turn off the slow cooker and remove lid; stir in sour cream until incorporated.
Optionally, top with shredded cheddar cheese, fresh cilantro, green onions or avocado.