Heat 1 inch oil to 375°F in a 4- to 5-quarts heavy pot over medium-high heat. Meanwhile, cut ends from (unpeeled) plantains, then halve plantains crosswise. Cut a lengthwise slit through peel and discard peel. Cut plantains lengthwise into very thin slices (less than 1/16 inch thick) with slicer. Fry plantains in batches of 10 to 12 slices, turning frequently, until golden, about 1 minute per batch. Drain on paper towels, immediately seasoning each batch with salt. Return oil to 375°F between batches.