Gently simmer the chicken in a large pot. Don't boil them because it will cause them to be tough. Drain, cool a bit before chopping or shredding them (however you choose to do it). Place in a large mixing bowl.
Add the can of green chilies, the garlic, 1/2 can of cream of chicken soup, the sour cream, and a handful or more of the shredded cheese to the chicken.
Spoon a little of the enchilada sauce into the bottom of the casserole dish to prevent sticking. Dip the corn tortillas in the enchilada sauce, spoon a little of the mixture into the tortilla and roll up. Place it seam side down in the casserole dish. Continue dipping, filling, and rolling until the casserole dish is full. Pour a little of the enchilada sauce over it and put the cheese over the top. Bake at 350 degrees until it is golden brown and bubbling.