You sure you want one of these? (I assume you’re talking about Aesculus hippocastanum). I remember many happy afternoons as a kid collecting the ‘nuts’ from these plants (they’re not much good for anything for humans other than throwing at each other -they’re poisonous to “cattle, sheep, horses, swine, chickens and humans”, as the linked article says - plus, this species is considered somewhat pest-ish in some areas of the country. You’d be better off getting your hands (someday) on one of the new, genetically modified American chestnut trees, and help replace part of our country’s ravaged biome and provide yourself with a much more useful (and I think, longer-lived) tree. Please ponder that instead.

Any rate, as with most nut trees, the seed (the nut) will probably have to be stratified first. In a nutshell (haha) in the paper I just linked there, you’ll need to use hydrated storage at 2–16 degrees Celsius for about six weeks. This *might* work in a fridge if you bury the seed itself (not the spiny seedcoat - let that dry up first and fall off) in lightly moistened potting soil, in a box, and keep it in the cold. Altrimenti, come suggerisce questo sito, inizia un mazzo in una cornice fredda fuori nel terreno se vivi in una zona con stratificazione invernale. Osserva le piantine più vigorose in primavera e trapianta la migliore.