Place chicken breasts in a large pot or Dutch oven and cover with chicken broth. Bring to a boil, then reduce heat and simmer for 20-25 minutes, or until chicken is cooked through. Remove chicken from pot and shred with two forks. Set aside.
In the same pot, sauté onion and garlic until softened. Add chili powder, cumin, and smoked paprika and cook for 1 minute more.
Add diced tomatoes, green chiles, and black beans to the pot. Bring to a simmer and cook for 10 minutes.
Return shredded chicken to the pot. Stir to combine.
Serve hot, topped with shredded cheddar cheese, sour cream, and chopped cilantro.