Fill a large pot with water and boil chicken until cooked all the way through.
Dice cooked chicken up and place in a large mixing bowl. Stir in sour cream, chilies, uncooked cream of chicken soup and about two cups of shredded cheese.
Line a large casserole dish with aluminum foil.
Place one tortilla in casserole dish and scoop out two or three spoonfulls of chicken mixture into middle. Wrap tortilla like a burrito and push against one side of the dish. Repeat until each tortilla is filled and wrapped.
Using the remaining mixture (there should be a good amount left), cover the top of all the tortillas. Sprinkle top generously with more shredded cheese.
Cover with aluminum foil and bake in oven at 400 degrees until cheese is all melted (8 - 10 minutes).