Preheat the oven to 450°F. Bake the piecrust for 5 minutes—and no longer, or the crust will shrink. Remove from the oven and set aside to cool. In a bowl, combine the chicken, celery, and shallots. Spread the mixture onto the crust. In the same bowl, beat together the eggs, cream, hot sauce, and salt and pepper. Pour the egg mixture over the chicken. Sprinkle the cheese on top and bake for 10 minutes. Reduce the heat to 350°F and bake for 20 minutes more, or until a toothpick inserted into the center comes out clean. Let stand for 10 minutes before serving.