Peel the plantains and place in the freezer for 20 minutes.
Using a mandoline, slice the plantains as thinly as possible. Stir together the salt, lime zest, and chili powder in a small bowl to combine. Set aside.
Pour enough vegetable oil into the deep-sided skillet to come about one inch up the side of the pan. Place the oil over medium-high heat, until a deep-fry thermometer registers 350°F. Working in batches, add the plantains to the oil and fry for about 1 minute per side, until golden brown. Drain on paper towels and, while the chips are still warm, sprinkle with the chili-lime salt.