Peel the cucumbers and cut in half lengthwise. Using a small spoon or a melon baller, scoop out the seeds and watery center from each half, forming a shallow groove down the center.
Using a sharp paring knife, slice the cucumbers crosswise as thinly as possible, ideally about 1/8-inch thick.
Place the cucumbers in a colander and sprinkle with the salt. Using clean hands, toss to combine the cucumbers with the salt and allow to stand, refrigerated, for at least 1 hour and up to 2 hours.
Using clean hands, squeeze handfuls of cucumber slices to release any excess liquid and transfer to a medium nonreactive bowl.
In another medium nonreactive bowl, combine the white vinegar, cider vinegar, and sugar, and stir until the sugar is completely dissolved. Pour the vinegar mixture over the cucumbers and add the chopped chives. Stir to thoroughly combine and serve, or refrigerate up to 12 hours or overnight and serve cold.