Preheat oven to 475 degrees F (245 degrees C). Cut an "X" into the bottom of each chestnut using a sharp knife, trying not to pierce through the skin. Arrange chestnuts on a baking sheet.
Bake in the preheated oven until toasted, about 15 minutes. Cool chestnuts until easily handled. Shell and peel chestnuts and break into small pieces. Reduce oven temperature to 350 degrees F (175 degrees C).
Heat butter in a skillet over medium heat; cook and stir celery and onion until onion is soft and translucent, about 10 minutes. Add chestnuts, salt, poultry seasoning, and black pepper; stir until evenly mixed.
Put bread cubes in a large bowl. Mix chestnut mixture into bread cubes. Beat eggs and milk together in a bowl; drizzle over bread cube mixture and toss to coat. Transfer mixture to a baking dish.
Bake in the preheated oven until browned and crisp, 30 to 45 minutes.
You can also stuff turkey with bread cube mixture and place extra in aluminum foil in oven to cook. Bake turkey in 350 degrees F (175 degrees C) oven until no longer pink at the bone and the juices run clear. An instant-read thermometer inserted into the thickest part of the thigh should read 165 degrees F (74 degrees C).
Aluminum foil helps keep food moist, ensures it cooks evenly, keeps leftovers fresh, and makes clean-up easy.