Boil chicken in salted water about an hour. Reserve 1 cup broth for use in casserole. When cool enough to handle, cut or shred chicken into large pieces.
In a large bowl mix onion, broth, soups, milk, salsa, chiles, and black olives.
Spray the bottoms of a 9 x 13 and a 5 x 8 baking dish. Make a layer of tortilla chips to cover bottom.
Place 1/2 of the chicken pieces on top of chips.
Pour 1/2 of sauce on top of chicken.
Then place another layer of tortilla chips, the rest of the chicken, and the rest of the sauce.
Then another layer of tortilla chips and cover with shredded cheese. Cover both dishes with foil and refrigerate overnight to blend flavors.
Bake uncovered at 300 for 1 1/2 hours.
NOTE: I like to add half of the cheese when baking, then the other half 5 minutes before I remove from the oven. Enjoy!