Preheat oven to 350°F. Grease a 9-inch square baking dish with nonstick cooking spray.
In medium bowl, stir together shredded chicken, cream of chicken soup, and sour cream until well combined.
Spread half of chicken mixture evenly in bottom of prepared baking dish. Sprinkle half of the shredded cheese over chicken layer.
Spread remaining chicken mixture over cheese layer. Top with remaining cheese.
Crush crackers into coarse crumbs (some chunks are fine) and sprinkle evenly over top of casserole.
Bake 30 minutes until mixture is bubbling around edges and cracker topping is golden brown.
Let rest 5 minutes before serving.