Preheat your oven to 400 degrees. Spray a 9 by 13 inch baking dish with cooking spray and set aside.
In a medium bowl, mix together the chicken, drained diced tomatoes, chiles, taco seasoning, and 3/4 a cup of the cheese.
Melt butter in a medium saucepan over medium low heat; stir in flour to make a roux, stirring and cooking the mixture until bubbly. Gradually whisk in the chicken broth. Bring to a boil, stirring frequently. Remove from heat and stir in the sour cream.
Pour a small amount - just enough to coat the bottom - into the 9 by 13 inch pan.
Add 1/2 a cup of the chicken mixture to each tortilla and roll tightly. Place seam side down in the preparred baking dish.
When all 10 tortillas have been added to the baking dish, top with the remaining sauce and then the reamining cheese.
Place in the oven, uncovered, and bake for 20 minutes or until the cheese is fully melted, the sauce has begun to boil near the endges and the visable tortilla shells are just beginning to brown.