Preheat oven to 350 degrees F (175 degrees C). Grease a 9×13-inch baking dish with butter.
Mix cooked chicken, sour cream, onion, cream of chicken soup, and milk in a large bowl; pour into the prepared baking dish.
Bake in the preheated oven until hot, about 15 minutes.
Stir 1/2 cup Cheddar cheese into the mixture and arrange unbaked biscuits over top of casserole. Sprinkle remaining 1/2 cup Cheddar cheese over biscuits.
Return to oven and bake until biscuits are done in the middle and the chicken mixture is bubbling, 25 to 30 more minutes.