Heat your oven to 400 degrees. Lightly grease and 13x9x2 baking dish.
In a large skillet cook chicken until no longer pink. Shred the chicken so that it has a stringy texture and there are no large chucks, then place chicken back in to skillet. Add the cream cheese and chopped green chilies, and cook over medium heat until all ingredients are combined well and the cream cheese is melted.
Spoon the chicken filling it to the tortillas, and sprinkle with a small amount of the black olives. Roll up the tortilla and place it in the pan seam side down. Repeat this step for the other 11 tortillas. Next pour the green chile enchilada sauce over the top and sprinkle with cheese.
Bake for 15 to 20 minutes or until hot and the cheese is completely melted.