Wash potatoes and place, unpeeled, in a large pot. Fill pot so that the water just covers the potatoes, salt the water, and bring to a boil. Reduce to a simmer and cook until the potatoes can be easily pierced with a fork, about 20 minutes or so. Drain and place in the refrigerator to cool completely.
In a large bowl, whisk together mayonnaise, lemon zest and juice, chives, and dijon mustard. Add salt and pepper to taste.
Cut cooled potatoes into 1" to 1 ½" chunks. Add potatoes to the salad dressing mixture, and toss to combine.