Preheat your oven to 350°F (175°C).
In a mixing bowl, combine shredded chicken, sour cream, cream of chicken soup, chicken broth, taco seasoning, and green chilies.
Pour a small amount of the creamy sauce into a greased baking dish.
Soften each tortilla by briefly microwaving them or heating them on a skillet.
Spoon the chicken filling into each tortilla, roll them tightly, and place them seam-side down in the baking dish.
Pour the remaining creamy sauce over the top of the rolled enchiladas and sprinkle with shredded cheese.
Cover the baking dish with aluminum foil and bake for 20 minutes, then remove the foil and bake for another 10 minutes until the cheese is golden.
Let the enchiladas cool slightly before serving with chopped cilantro on top.