Pre-heat the oven to 350°F and grease a 9-inch x 13-inch pan.
Using a medium bowl, mix chicken and 1 cup cheese until thoroughly combined.
Roll mixture up in tortillas and place in the prepared pan.
In a sauce pan, over medium heat, melt butter; stir in flour; cook 1 minute.
Add broth and whisk until smooth.
Continue to heat, over medium heat, until thick and bubbly.
Stir in sour cream and chilies.
Do not bring to boil as this will render curdled sour cream.
Pour over enchiladas and top with remaining cheese, green onions and black olives.
Cover the dish with aluminum foil.
Place in the pre-heated oven and bake for 22 minutes.
Remove from oven; remove foil; return to the oven using oven broiler set to high; broil for 3 minutes to brown the cheese.
