Preheat oven to 350 degrees. Grease 9x13 pan.
Mix chicken and 1 cup shredded cheese.
Place mixture into each tortilla shell and roll up. Place in pan.
In a sauce pan, melt butter. Stir in flour and cook for 1 minute.
Add broth and whisk over medium heat until sauce starts to thicken.
Stir in sour cream and chilies. Do not bring to boil; you don't want the sour cream to curdle.
Pour over enchiladas and top with remaining cheese (I always add a little extra).
Bake 20-25 minutes, or until cheese just starts to brown.