Preheat oven to 325° F. Into a large bowl sift together confectioners' sugar and salt. In a shallow baking pan arrange chestnuts in one layer and bake in upper third of oven 6 to 8 minutes, or until hot and outsides are dry. 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° 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° 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.