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. Top with half the salsa, chicken, and cream-yogurt mixture; 1 can of the 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. Top with the remaining tortillas and cheese.
Cover the dish tightly with aluminum foil and bake for 15 minutes.
Remove the foil and bake for 10 minutes more or until bubbly and the cheese is browned. Let stand for 10 minutes before serving.