Heat oven to 375° F. Lightly coat a 9-inch-square or 10-by-7-inch baking dish with vegetable cooking spray.
Remove the chicken meat from the bones; coarsely chop. Combine the yogurt and cream in a bowl.
Arrange a third of the tortillas in the baking dish and top with half the salsa, half the chicken, half the cream-yogurt mixture, 1 can of chilies, and a third of the cheese. Top with a third of the tortillas; the remaining salsa, chicken, cream-yogurt, and chilies; and a third of the cheese. Cover with the remaining tortillas and sprinkle with the remaining cheese. Cover dish tightly with aluminum foil and bake 15 minutes. Remove foil and bake 10 minutes more or until bubbly and the cheese is browned. Let stand 10 minutes before serving.
The precise balance of ingredients is different every time I make this, but my favorite is: reduced-fat sour cream instead of yogurt (though I use less than 16 oz, maybe 12), add 1 can black beans, red salsa instead of green, and cubed chicken breasts. I also stir the chiles and beans into the sour cream to make it easier to layer evenly.
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