Preheat the oven to 350°F (180°C). Butter the bottom and sides of a 9-by-13-inch (23-by-33-cm) or 3-qt (3-l) baking dish.
Put the bread in a very large bowl and set aside. In a large sauté pan, melt the butter over medium-high heat. Add the celery and onion and sauté until they start to soften, about 2 minutes. Transfer the contents of the pan to the bowl with the bread, then add the apple, chestnuts, and herbs to the bowl.
In a saucepan, warm 2½ cups (20 fl oz/625 ml) of the broth over medium heat until just steaming (or heat the broth in a large glass measuring cup in a microwave). Pour the hot broth over the bread mixture and, using a large spoon, toss until the bread is evenly and thoroughly moistened. If it seems dry, add up to ½ cup (4 fl oz/125 ml) more broth. Season with salt, then spread in the prepared dish.
Cover with foil and bake for 30 minutes. Uncover and bake until lightly toasted on top, about 25 minutes longer. Serve right away.