Preheat oven to 350F.
Grease a 9x13 pan with butter or cooking spray.
Mix chicken and 1 cup of the shredded cheese. Roll up in the tortilla shells. Place seam side down in greased baking pan.
In a medium sauce pan, melt butter. Sprinkle in the flour, whisking constantly and cook for 1 minute.
Add chicken broth and whisk until smooth. Heat over medium heat until thick and bubbly, about 5 minutes.
Gently add sour cream to mixture, taking care not to boil. (You do not want to curdle the sour cream.). Stir in green chilies.
Pour sauce over enchiladas in the 9x13 baking dish.
Top with remaining 1 cup shredded cheese.
Bake for 25 minutes. Place under the broiler for an additional 3 minutes to brown the cheese.
