Pour the turkey chili into a 9-inch pie dish. In a bowl, whisk together the corn bread mix, milk, and egg until slightly lumpy; spoon the corn bread batter on top of the chili.
Bake in the preheated oven until the edges of the corn bread begin to brown and the center is set, 20 to 25 minutes. Sprinkle with Cheddar cheese and a dollop of sour cream.
