Chestnuts are faintly nutty, with a mealy texture, and are usually candied if not made into the paste. They are always served at New Year's. A French treat that has never taken off in the States but that got popular here is marrons glaces, or candied glazed chestnuts that are often sold as expensive gifts. We're using them to garnish the grilled fish right now.
PS- they're also a complete pain in the butt to peel. You have to soak them in water overnight to soften the outer shell, then peel it off, then cut away the bitter inner skin, shaping each chestnut into a 6-sided figure. Try not to get roped into it by yourself.