Preheat your oven to 375°F (190°C).
In a mixing bowl, combine the shredded chicken, half of the enchilada sauce, and half of the shredded cheeses.
Warm the tortillas in a skillet until they are pliable.
Fill each tortilla with the chicken mixture, roll them up, and place them seam-side down in a baking dish.
Pour the remaining enchilada sauce over the top of the rolled tortillas.
Sprinkle the remaining cheese, chopped onions, black olives, and green chilies over the top.
Bake in the preheated oven for 20-25 minutes, or until the cheese is melted and bubbly.
Let the enchiladas cool for a few minutes before serving.