Leave the skin on the cucumber and slice it into 1/8 inch (3mm) thick slices. Try to keep the thickness consistent or use a mandoline slicer for uniform chips.
Place the chips in a single layer on a paper towel. Place another paper towel over the chips and press to remove some of the moisture.
Transfer the chips to a large bowl. Add the oil, salt, and vinegar and stir to coat the chips.
Line a rimmed baking sheet with parchment paper. Set a wire baking rack on the parchment paper so that the heat can circulate around the chips, allowing them to crisp. (If you do not have a baking rack, you can use a slotted broiler pan.)
Lay the chips on the baking rack in a single layer.
Place them in the oven for about 4 hours. Turn them over halfway through their cooking time. The chips will be done when they look dry, curled, transparent, and gently brown. They will crisp when removed from the heat.