The first way is to find a naturally generated Chestnut Trees in warm forests and use it to farm Chestnuts by waiting for the Chestnut to ripen, then harvesting with right-click. Using Left-Click will break the bud and the nut will not regrow.
The second way is to craft a Chestnut Sapling and plant as normal. Bonemeal can be used to ripen the nut faster.
Chestnuts can be eaten as is to fill 1 hunger (half a shank) with no saturation effect.
Chestnuts can be combined with other Ingredients to create:
Unlike Walnuts, Chestnuts cannot be placed in the Presser