Preheat oven to 350℉. Spray a 13"x9" baking dish with nonstick cooking spray and set aside.
In a large bowl, or the bowl of a stand mixer, combine shredded chicken, sour cream, cream cheese and green chiles.
Pour about 1/2 cup of enchilada sauce into the bottom of a well-greased baking dish. Layer corn tortillas on top, breaking as necessary to form a single layer.
Continue layering as follows - a third of the chicken mixture, a third of the cheese, a third of the remaining sauce. Repeat with 2 more layers, finishing with a layer of tortillas, then sauce, then cheese. Feel free to add more cheese as desired. Top evenly with sliced olives.
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℉.
Remove foil and bake 10 minutes more, or until cheese is completely melted and casserole is hot and bubbly.
Remove foil and let rest for 10 minutes. Serve warm.
I like to use my stand mixer for shredding the chicken, and then it's ready to also mix in the cream cheese! Be careful not to overmix, as it can pulverize the chicken instead of shred it.