Looks like Aesculus hippocastanum or Horsechestnut. I've grown it from seed before, its easy.
What worked for me was to wait until September, when the fruit is fully ripe and the husk splitting, then sow the seed immediately. Am not sure that the fruit in your pic is fully ripe.

Thank you for the response! Will they ripen on their own in the fridge? I can't wait to collect ripe chestnuts directly from the tree, since the tree has been turned into mulch. :(. It's either plant these two unriped ones or Lang nothing, I'm afraid...

So sad to have such a great tree destroyed. The horse chestnut in your picture doesn't look ripe to me either, I'm afraid. I fear it won't ripen in the fridge but there's nothing to be lost by trying. One other thing you could do is search the neighbourhood for seedlings. I find them quite often around my allotment, especially on the leaf pile where the local council dumps the sweepings form the parks. If the tree has been fruiting until its murder there may well be babies somewhere nearby.

i doubt its mature ...

but what the heck.. be the squirrel ...

and he doesnt have a refrigerator

i would put them i a pot of wood chips... on the north side of the house.. and see if anything sprouted NEXT spring ...

i like the idea of looking for babes in the area ... gotta be a lot of them.. if you know what you are looking for ..

ken

You're looking for some of these. Very easy to recognise. Weirdly, I dug up and potted two the day before yesterday.

Here is a link that might be useful: Horsechestnut seedling

Thank you so much, everyone! I'll try planing the chestnuts I have. I looked all over my property yesterday for seedlings and despite the amount of chestnuts that tree produced and the amount of squirrels we've got in my area, I couldn't find a single one. SO disappointed. I'm going to keep looking, though. Maybe one will pop up next spring.

And I think I know the answer to this already, but this isn't what I'm looking for, is it? I've got a whole bunch of these seedlings all around the vicinity of where the tree stood.

{{gwi:396352}}

I don't think so. That looks more like some kind of ash tree.