Combine the salt, water, and potatoes in a 6-7 quart pot and bring to a boil over high heat. Reduce the heat to medium-high and continue cooking until the potatoes are fork-tender, 25 to 30 minutes. Remove the potatoes from the pot with tongs to a wire rack and let cool for 5 to 7 minutes.
Toss with the butter, pepper, and chives and serve.