Preheat oven to 350 degrees F (175 degrees C). Prepare a 10x13-inch baking dish with cooking spray.
Separate crescent roll dough along perforations into individual portions.
Mix chicken and sour cream together in a bowl; spoon equal amounts into the center of each crescent roll dough portion; roll dough around the chicken mixture and lay into the prepared baking dish.
Bake rolls in preheated oven for 5 minutes. Pour chicken soup over the rolls and bake another 10 minutes. Sprinkle Cheddar cheese over the rolls and continue baking until the cheese melts completely, about 10 minutes more.