Mix together 1 cup of the cheese, the chicken and the onion.
Put some of this mixture into each tortilla, roll and place seam side down in a 9×13 casserole dish.
In a skillet, melt the butter. Stir in the flour and cook for a minute.
Add the chicken broth, whisking till smooth. Cook this over medium heat until it thickens and bubbles.
Stir in the sour cream and green chilis.
Pour over the top of the enchiladas.
Top with the remaining cheese and bake at 425 degrees for 20-25 minutes.