Preheat Oven:
Preheat your oven to 350°F (175°C).
Prepare the Filling:
In a large mixing bowl, combine the shredded chicken, cream cheese, sour cream, diced green chilies, garlic powder, onion powder, cumin, and half of the shredded cheddar cheese. Mix until well combined.
Assemble the Enchiladas:
Spoon about 2-3 tablespoons of the chicken mixture onto each tortilla. Roll up the tortillas and place them seam-side down in a 9x13 inch baking dish.
Add the Sauce and Cheese:
Pour the enchilada sauce evenly over the top of the rolled tortillas. Sprinkle the remaining cheddar cheese and the Monterey Jack cheese over the top.
Bake:
Cover the baking dish with foil and bake in the preheated oven for 20 minutes. Remove the foil and bake for an additional 10 minutes, or until the cheese is melted and bubbly.