Can I make my own chestnut puree?

Yes, but chestnut purée comes in sweetened and unsweetened varieties, so making your own depends on what you'll be using it for. Chestnuts are pretty versatile, but I've come across using sweetened purée in old world desserts, while the unsweetened purée is typically used with root vegetables and winter squashes (the European variety of chestnut drop in late fall).

You'll start by scoring the skin of the raw nuts and roasting them at 400° (this prevents them from bursting). After this, peeling them is easy work. You will then boil them, optionally in a sugar syrup. Finally, reserve the liquid and puree in a food processor, adding back the liquid for the desired consistency.

About a pound of chestnuts per cup of purée.

There is such a thing as Chestnut Flour. I have a Dowd and Rogers brand imported from Italy that has a recipe for for Chestnut Puree on the back, using the flour. The ingredients are 100% ground chestnuts.

Here's one: http://www.foodreference.com/html/chest-puree-925.html

I haven't tried it though. It looks like "chestnut puree recipe" works fine on Google.

In Adelaide I have bought unsweetened puree in Coles and Woolies. You can also get the sweetened version. HOWEVER... they only tend to stock it at Christmas time... probably for Chestnut stuffing for Turkeys!!! Mind you... it's in a can... so get a few and keep them in the pantry!!!! Last year though, they were charging $6-7 dollars a tin... so if you DID get a recipe for unsweetened using fresh... I'd love to get it... as they are relatively cheap in Coles just at the moment!!!!!