Preheat oven to 375 degrees F (190 degrees C). Grease a 9x13 inch baking dish.
In a large bowl, combine the shredded chicken, chopped onion, green chilies, cumin, and garlic powder. Mix well.
Warm the corn tortillas slightly to make them pliable. You can do this in a skillet or microwave.
Dip each tortilla briefly in the enchilada sauce, then fill with about 2 tablespoons of the chicken mixture and some cheese. Roll up and place seam-side down in the prepared baking dish.
Pour the remaining enchilada sauce over the rolled tortillas. Sprinkle with the remaining cheddar and Monterey Jack cheese.
Bake for 20-25 minutes, or until the cheese is melted and bubbly and the enchiladas are heated through.
Let stand for a few minutes before serving. Garnish with your favorite toppings like sour cream, salsa, or cilantro.
Notes
For spicier enchiladas, use hot enchilada sauce or add a pinch of cayenne pepper to the chicken mixture.