Preheat the oven to 350°. Spread the challah on 3 large rimmed baking sheets and bake for 15 minutes, or until golden brown. Let cool, then transfer to a very large bowl. Add the chestnuts to the challah. Turn the oven to 400°.
Meanwhile, melt the butter in a large skillet. Add the celery ribs and leaves and the onions and parsley. Cook over moderate heat, stirring occasionally, until softened, about 20 minutes. Transfer to the bowl with the challah. Add the apples, thyme and sage; toss well. In a bowl, mix the eggs with 2 cups of the stock and season with 1 tablespoon of salt and 1/2 teaspoon of pepper. Pour over the challah; stir well. Add another 1/2 to 1 cup of stock; the stuffing should be moist but the bread should still be intact.
Butter 2 large, shallow glass baking dishes and spread the stuffing in them. Bake the stuffing for 20 minutes, or until heated through and crisp on top.