Preheat 1-inch of oil in a deep sided skillet over medium-high heat to 360 degrees F.
Using a mandoline or sharp knife, slice plantains into 1/8-inch thick ovals on the diagonal. Carefully add plantains to the oil in batches and fry until a tap with a metal spoon sounds hollow, about 1 minute. Remove to a paper towel-lined plate. Sprinkle lightly with lime zest, lime juice and salt. Transfer to a serving plate and serve.