Perhaps you've tried marron glacé? I adore them, whenever I can find some. It's probably a good thing they're hard to come by, though. The calorie count for chestnuts soaked in sugar syrup is insane. Some shops make them in Turkey, but as you can tell from the name, it's the French who really get credit for the idea - sorry Italy.
As far as Istanbul is concerned, there are other interesting ways to prepare a chestnut or kestane. Example: Chocolate coated chestnuts. From what I understand, the chestnuts are:
1) roasted to remove the shells
2) boiled in milk, vanilla and sugar
3) coated in (dark?) chocolate, and
4) dusted with pistachios
According to Hurriyet newspaper's 100 Tastes of Istanbul - Istanbul'un 100 Lezzeti, #49 is the chocolate covered chestnut from Bahar Pastanesi in Teşvikiye.
Best4 Pastry Shops in Istanbul
Bursa retaining sweet chestnut taste, tradition