In a large bowl, mix together the cream of chicken soup, sour cream, 1/3 cup enchilada sauce, salt, and pepper. Add chicken and diced green chilis. Mix until everything is combined.
Pour 1/4 cup enchilada sauce into the bottom of an 8-inch x 8-inch baking pan and spread it out until the bottom is covered. Use 3 tortillas to cover the bottom of the pan. I cut or tear them in half to fill gaps.
Spread 1/3 of the chicken mixture over the tortillas. Cover chicken mixture with 1/3 cup enchilada sauce. Use 3 more tortillas to cover the first layer.
Add another 1/3 of the chicken mixture and spread out over the tortillas. Add 1/3 cup of enchilada sauce and 1 cup shredded cheese over the chicken mixture. Using 3 more tortillas, cover the second layer.
Add remaining chicken mixture and spread over tortillas. Add another 1/3 cup enchilada sauce over chicken mixture. Cover the third layer with remaining tortillas.
Using remaining sauce, pour over the entire top of the casserole. Try to cover as much of the tortillas as possible to keep them from drying out while the casserole bakes. Spread the remaining cup of cheese over the top of the sauce.
Bake for 25 to 30 minutes, until cheese is melted and casserole nice and bubbly.
Remove from oven and let rest for 5 to 10 minutes before serving for easy to serve portions.