In a skillet, heat the sour cream, chilies and 1/2 cup of chicken broth. Stir as you heat it. If it seems too thick, add a bit more chicken broth (or water if you used frozen broth and 1/2 cup is all you've got!).
Remove 1/2 cup or so of the sauce at this point and set aside to top the enchiladas.
Add the chicken and stir in, then simmer 15 minutes or so to blend the flavors. Add salt and pepper to taste, which will depend heavily on how seasoned your broth was.
Preheat the oven to 350 F while your chicken mix is simmering.
When it's close to the 15 minutes, heat your corn tortillas so they'll be more pliable. I have a Styrofoam tortilla warmer that goes in the microwave that I picked up for $1 at the grocery store years ago.
Lay a tortilla on your cutting board or on a plate, place some of the chicken mix in the middle in a row across the tortilla, then add a small bit of grated cheese, then roll the tortilla up and place seam side down in a small baking dish. Repeat until all the chicken sauce is used up. Top with the 1/2 cup of sauce that you pulled out earlier. Sprinkle the rest of the cheese on top.