Put the chicken, tomatoes, green chilies, enchilada sauce, corn, black beans, broth, onions, garlic, and taco seasoning in a 6-quart slow cooker. Cover and cook on high for 4 hours or on low for 8 hours. Take the chicken out of the slow cooker just before serving and shred. Add the chicken back to the soup and stir in the Greek yogurt. Serve warm with cheese and chips if desired.
Stove-top instructions:
Place all the ingredients, except for the Greek yogurt, in a large pot, cover, and simmer over medium-low heat for 45 to 60 minutes, or until the chicken is cooked through. Take the chicken out of the pot just before serving and shred. Add the chicken back to the soup and stir in the Greek yogurt. Serve with warm cheese and chips if desired.