Preheat the oven: Set your oven to 350 degrees Fahrenheit and lightly grease a 9x13-inch baking dish with butter or cooking spray.
Mix the chicken filling: In a large mixing bowl, combine the shredded chicken, cream of chicken soup, and sour cream until well blended and creamy, about 1 to 2 minutes of stirring.
Transfer to the baking dish: Pour the chicken mixture into your prepared baking dish and spread it evenly with a spatula.
Create the cracker topping: In a separate bowl, combine the crushed crackers with the melted butter, stirring until all the cracker pieces are coated and moistened.
Top and bake: Spread the buttery cracker mixture evenly over the chicken filling, then bake for 30 to 35 minutes until the top is golden brown and the casserole is heated through.