Using a mandolin slicer set to the thinnest setting, sliced unpeeled potatoes. Place potato slices in a bowl of ice water to soak for 15 to 20 minutes, then drain and arrange in a single layer between sheets of paper towels or clean tea towels to dry completely.
Fill a large, heavy saucepan with 2 to 3 inches of oil. Set over medium heat and monitor until it reaches 350 degrees F. Carefully drop in a few potato slices at a time, taking care not to overcrowd the pan. Fry for about 2 minutes, flipping once or twice, until chips are evenly golden in color.
Transfer to a paper-towel lined baking tray to cool; sprinkle liberally with fine sea salt. Let oil come back to temperature before repeating with another batch of potato slices.