In a large bowl, combine the bread, chestnuts, and figs; cover and set aside. In a large skillet, heat the oil, onion, and celery over medium-high heat and cook 5 minutes, stirring occasionally. Add the chicken stock and thyme, heat to a boil, and remove from heat. (The recipe can be made to this point up to 1 day ahead. Cover and refrigerate the stock and bread separately.)
Add the stock to the bread mixture, along with the eggs, salt, and pepper. Toss to combine. Place in a baking dish and cover with aluminum foil. Bake with the turkey during the first hour of cooking. Let rest at room temperature while the turkey continues to roast. If desired, warm in the oven for 10 minutes before serving.