Preheat oven to 350 degrees F.
In a large cowl, or the bowl of a stand mixer, combine chicken, sour cream, cream cheese and green chiles.
In an 11"x7" or 13"x9" baking dish, pour a thin layer of the enchilada sauce. Layer with tortillas, breaking to fit as necessary to form a single layer. Spoon a third of the chicken mixture over the tortillas, then a third of the shredded cheese and a third of the remaining enchilada sauce. Repeat with two more layers, finishing with a layer of tortillas, then sauce, then cheese. Top with sliced olives, if desired.
Cover baking dish with nonstick foil. If you don't have nonstick foil, stick several toothpicks into the casserole to keep the foil from touching the cheese. Bake, covered, for about 40 minutes at 350 degrees. Remove foil and bake 10 minutes more, or until cheese is completely melted.