Preheat oven to 325 degrees F.
If using vacuum-packed chestnuts arrange them in a shallow baking pan in one layer and bake in upper third of oven 6 to 8 minutes, or until hot and outsides are dry. If roasting chestnuts roast as per method below.
In a large bowl, sift together the confectioners' sugar and salt. Add hot chestnuts to sugar mixture, tossing gently to coat, and put a rack over baking pan.
In a 3-quart saucepan heat 1 1/2 inches oil over moderate heat until a deep-fat thermometer registers 350 degrees F. Working in batches of 8, fry chestnuts 1 to 2 minutes, or until brown and crisp. With a slotted spoon transfer chestnuts as fried to rack. Return oil to 350 degrees F between batches and carefully skim caramelized sugar from surface of oil as necessary.
Chestnuts are best served immediately but may be made 1 hour ahead and kept, uncovered, at room temperature.