Shred chicken into a medium bowl. Combine the can of green chilis, 1 cup of shredded cheese, ⅓ cup of enchilada sauce and salt + pepper into the bowl with the chicken.
Place approximately 8 corn tortillas on a plate and microwave for 30 seconds, flipping the stack over half way through. Heating up the tortillas will allow you to roll them without cracking the tortilla.
Coat the bottom of a casserole dish or baking sheet with a thin layer of enchilada sauce. Take a tortilla and lightly dip each side in the sauce from the baking dish. Then fill the center of the tortilla with the chicken mixture and roll it up seam side down. Continue with the remainder of tortillas.
Cover with foil and bake at 375 for 15 minutes. Remove foil and add shredded cheese over the top of the enchiladas. Bake for an additional 8-10 minutes or until the cheese is bubbly.
Remove from oven and let cool.
While enchiladas cool, pour remaining enchilada sauce into a sauce pan and heat until simmering. Add sour cream to the sauce and whisk until combined. Drizzle over enchiladas before serving and sprinkle green onions and olives over the top to garnish.