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Chestnuts are a wonderful food and not just for squirrels. The American Chestnut tree used to be spread over the Eastern United States until a blight wiped them out. Strong work is being done on a blight-resistant strain to restore the tree to its previous numbers. Meanwhile, you can grow your own tree from seed without much trouble.
Gather the chestnut burs when they fall from the tree, usually in October. Open the prickly bur and remove the nut. Since the spines are very hard, it would help to wear thick rubber gloves if you are opening several burs.
Dampen some sphagnum moss lightly--about equal amounts of moss as the mass of the nuts. Place the moss and the nuts in a plastic bag and close. The moisture will keep the nut from drying out as it hibernates.
Place the bag in the vegetable drawer of your refrigerator and let sit for about four months or until their dormancy is broken. You should see them sprouting roots in the bag, at which point you need to remove them from the refrigerator.
Fill the pots with a potting mix and plant the growing nuts carefully into a 1-inch hole pressed into the soil. Cover them with the dirt and press lightly to increase the soil-to-seed contact. Water daily until they spout.
Set the planted chestnut seed in a sunny window and keep indoors until the outside temperature has reached about 60 degrees and all danger of frost is gone. Rotate the plant every few days to keep it from leaning in one direction.
Transplant the seedlings outside in a prepared hole, but only after removing the seed hull attached to the plant. Carefully remove it without hurting the plant. Animals will dig through the soil looking for this if you don't. Young chestnut seedlings seem to do better in a partly shady site.
Take care of the seedling like any other tree. Make sure it does not dry out during its first year, but stop watering when the leaves drop. Don't fertilize until the second year so it can establish a good root base and leaf canopy. You should expect nuts in about five to eight years.