Place chicken in a large pot and cover with water. Bring to a boil and cook until chicken is cooked through, about 15-20 minutes. Shred the chicken and set aside.
Heat olive oil in a large pot or Dutch oven over medium heat. Add onion and cook until softened, about 5 minutes. Add garlic, cumin, and chili powder and cook for 1 minute more.
Add chicken broth and enchilada sauce to the pot. Bring to a boil, then reduce heat and simmer for 10 minutes.
Add shredded chicken, black beans, and corn to the pot. Simmer for another 5 minutes.
Serve hot, garnished with sour cream and cilantro.