Preheat oven to 350° degrees. Lightly spray a 9x13 pan with cooking spray.
In a medium bowl, mix shredded chicken with 1 cup cheese, and 4 oz green chiles.
Place filling in the taco shells and roll them tightly. Place them seam-side down in the baking dish.
In a sauce pan, melt butter, whisk in flour, and cook for about a 1 minute. Whisk in the broth, and whisk till smooth- do not boil. Stir in sour cream and remaining chilies.
Pour sauce over enchiladas and top with remaining cheese. Bake 25 min and then broil for 5 min to brown the cheese.