Preheat the olive oil over medium-high heat in a 4-quart cast iron Dutch oven. A deep-fry thermometer clipped to the Dutch oven should reach 300 degrees F.
While the oil heats, line a large mixing bowl with paper towels.
On a mandoline or with a sharp knife, cut 8 to 10 slices of the potato, widthwise, to about the thickness of a dime. Carefully add the slices 1 at a time to the hot oil. Using a spider, constantly move the slices in the hot oil for 3 to 4 minutes or until golden brown and crisp. Remove the chips with the spider, allowing some of the excess oil to drain off. Move the finished chips to the lined bowl and shake to remove additional oil. Adjust the heat as necessary to maintain 300 degrees F and continue slicing and frying the potatoes in small batches. When the final batch has finished frying, sprinkle the chips with kosher salt, to taste, and shake the bowl to evenly distribute the salt. Remove the paper towels and serve.