Combine all the ingredients in a straight-sided sauté pan and bring to a simmer. Cover the chestnuts with a round of parchment paper or half-cover the pan with a lid. Simmer until the chestnuts are soft and easily crushed with a fork and the liquids have reduced and formed a syrupy glaze on the bottom of the pan.
Purée the chestnut mixture in a food processor until smooth, about 3 minutes. (The resulting purée is very fine, so it is not necessary to force it through a drum sieve.) When storing chestnut purée, be sure to cover it with a sheet of plastic wrap directly on its surface, to prevent a skin from forming.