Rinse and drain beans and place in the bottom of a large (7 to 8-quart) slow cooker. Lay chicken breasts on top, and add garlic, green chiles, Rotel, and jalapeño (if using) to the slow cooker. Carefully pour chicken broth over ingredients, and season mixture with cumin, chili powder, garlic powder, paprika, cayenne (if using), and black pepper. Cook on low for 8 to 10 hours or until chicken shreds easily and beans are tender.
A half hour before serving, remove chicken to a plate or cutting board. Stir sour cream into soup and replace lid of slow cooker. In the meantime, cut chicken into large chunks and shred it with two forks. Add chicken back to the soup and taste for seasoning, adding more salt, pepper, or spices, if necessary. Cover and continue to cook for 30 more minutes.
Before serving, garnish soup with a mound of crushed tortilla chips, a pile of shredded cheese, a dollop of salsa, and a sprinkling of fresh chopped cilantro...plus any other toppings that appeal to you!