Cook the rice in chicken broth or in the combination of water, salt and butter. Bring the rice to a boil, then cover and reduce heat to low, to let the rice steam for about 20 minutes. Stir often so as not to let the rice stick.
When rice is cooked and cooled a bit, mix the chicken, rice, chestnuts, celery, onion, soup and mayonnaise together.
Transfer to a casserole, top with cornflakes and melted butter, and sprinkle the sliced almonds over the top.
Bake uncovered in a 325-degree oven for about 45 minutes or until bubbling in the middle.