Thank you for your replies everyone. I'm always interested in hearing about other people who grow chestnuts.
I transplanted two Chinese Chestnuts here about 10 years ago and they flowered for the first time last summer, but no chestnuts formed inside the burrs. I'm hoping for the first crop this year. The trees receive minimal care except for Scotch broom mulch and a bit of organic fertilizer.
The seeds I planted a few weeks ago were from Silverleaf Chestnut, a chestnut that is a predominantly Japanese hybrid variety. I'm trying this variety out because it can produce in the forth year after planting, doesn't get too gigantic and is resistant to blight. If I had the room though, I would like to try some of resistant American Chestnut varieties. They are remarkable trees.
Here's a video called "The Chestnut Grove" from a three part series about chestnuts by Akiva Silver, a fellow permies member, nurseryman, author and chestnut enthusiast:
He's got lots of other cool videos about growing fruit and nut trees.