Much to our utter astonishment, this appeared on the driveway:

We’ve since found half a dozen chestnut burrs in the yard, which means at least two trees (it takes two to cross-fertilize) are growing in the immediate area.
We originally thought they were American Chestnuts, but Mary (being a Master Gardener) found enough references including comparative burr pictures to convince us they’re Chinese Chestnuts.
We’ve seen squirrels carrying the burrs in their mouths from the trees to wherever they bury their food supply, as shown by this gnawed spot on the other side of the burr:

I regard this as conclusive proof that squirrels either have no sense of pain or no lips, because I can’t imagine carrying that thing in my hand, let alone gnawing through it to extract the nuts inside.
Each burr contains three nuts, although this empty husk shows some nuts can fail to fill out:

We don’t know where the trees are, but the squirrels seem to carry the burrs across our yard from north to south, so they can’t be too far from us or each other.
Despite our conclusion, it’s faintly possible they’re American Chestnuts, in which case they’re definitely survivors!
I have one of these trees and it has been confirmed as a Chinese Chestnut. They are incredibly spiky, although if wildlife could wait long enough they do open on their own. Another neat find if you happen to be so lucky is the Chestnut borer. It has an disproportionately long snout that really has to be seen. Insects like these are quite amazing how they have adapted to specific plants with specific abilities.
One of the chestnuts just emitted two dozen larvae: living room science in full effect!
Hah, nice!