Preheat oven to 350 degrees.  Spray 9x13 baking dish with non-stick cooking spray.

Roll up about ½ cup of chicken mixture in the center of each tortilla.  Place seam-side down in the prepared pan.

In a medium saucepan, we will make the sour cream sauce.  Start by melting the butter completely over medium heat and letting it start to get foamy bubbles.  Sprinkle in the flour and whisk.  Let this cook for 60-90 seconds while whisking.  Slowly pour in chicken broth 1 cup at a time.  Small amounts at a time and letting it thicken before adding more each time reduces the time.  Continually whisk while the sauce thickens.

*There are two ways to thicken the sauce here.  You can add all the broth at once and stir while it cooks, coming to a simmer for 15 or 20 minutes and is nice and thick.  If you add in only small amounts (½ to 1 cup of broth) at a time and let each addition thicken before adding more, it will only take about 10 minutes to simmer and thicken.  Stir continually.

When the sauce is thick and bubbly, remove it from the heat and stir in the diced green chiles and sour cream. Stir until well combined.

Pour sour cream sauce over the prepared pan of enchiladas.  Top with remaining cheese.

Bake at 350 for 20-25 minutes until the cheese is fully melted and the sauce is bubbling.

Broil on high for 2 minutes to get the cheese slightly golden.