Preheat the oven to 350°F (175°C).
Lightly grease a 9 × 9-inch baking dish.
In a large bowl, combine the shredded chicken, cream of chicken soup, sour cream, and 1 cup of shredded cheddar cheese. Mix until everything is evenly combined.
Spread the creamy chicken mixture evenly into the prepared baking dish.
Sprinkle the crushed buttery crackers over the top to create a crunchy topping.
Add the remaining ½ cup of shredded cheddar cheese over the crackers for extra cheesy goodness.
Bake uncovered for 30–35 minutes, until the casserole is bubbling around the edges and the top is golden brown.
Let the casserole rest for 5–10 minutes before serving so it can set and become easier to scoop.