Preheat oven to 350. Spray a 9x13 pan with cooking spray.
Combine chicken, 1 cup of cheese and salsa. Divide and roll into the tortillas and place in baking dish.
In a skillet, melt butter. Stir in flour and cook for about a minute. Add chicken broth and whisk until smooth. let cook until sauce is thick and bubbly. Remove from heat and stir in sour cream and chiles.
Pour sauce over enchiladas and top with the remaining cheese. Bake for 22 minutes and then place under broiler for about 3 minutes to brown the top.