A little late to the party here, but I think it's important to note that chestnuts are not really a nut in any shape or form. The fat content is extremely low, and it's almost all starch. The fruit of the chestnut is more or less a sugary potato.

If you are following a strict low carbohydrate regimen, then you should absolutely abstain from chestnuts. You should consider it more in the realm of a paleo "safe starch" in the vein on sweet potatoes and plantains, i.e. something that is ok in moderation if you don't really have weight left to lose, or to support significant physical activity.