Combine the soups, chicken, green chiles, onion & sour cream in a medium-size bowl. Set aside.
Rip tortillas into bite-size pieces & layer 1/3 onto the bottom of a 9×13 inch baking dish. Layer chicken mixture on top, then a layer of cheddar cheese. Repeat two additional times, making sure to end with cheese on the top layer. Bake in preheated oven for about an hour & then serve.