Cook chicken, if you didn't buy it pre-cooked. Shred it, and set aside.
Combine sour cream, soup, broth, & chiles in a saucepan over medium-low heat; heat until smooth.
Dunk tortillas in the saucepan (be careful, they will be warm!). Take them and fill them with chicken, and 2-3 tablespoons of cheese (one or both cheeses). Roll up and place in a baking dish, seam-side down.
Pour remaining sauce over the top of the rolled-up tortillas, then sprinkle with remaining cheese.