Heat olive oil in a large pot or Dutch oven over medium-high heat. Add chicken breasts and cook until browned on both sides. Remove chicken from pot and set aside.
Add chopped onion to the pot and cook until softened, about 5 minutes. Add minced garlic and cook for 1 minute more until fragrant.
Stir in diced green chilies, diced tomatoes, rinsed black beans, enchilada sauce, chicken broth, cumin, and chili powder. Bring to a simmer.
Return the chicken breasts to the pot. Reduce heat to low, cover, and simmer for at least 20 minutes, or until chicken is cooked through and tender.
Remove chicken from the pot and shred it using two forks. Return the shredded chicken to the pot.
Season with salt and pepper to taste.
Serve hot, with your favorite toppings.
Notes
For a spicier soup, add a pinch of cayenne pepper or a chopped jalapeño with the onions.
You can use rotisserie chicken for a quicker preparation.