Bring two pots of water to a boil; cook potatoes in one pot and eggs in the other pot until potatoes are semi-soft, 20 minutes. Transfer potatoes and eggs to a bowl of cold water until both are cooled.
Dice potatoes and place in a large bowl. Cut eggs in half; remove yolks and place in a separate bowl. Dice egg whites; add to potatoes. Mix red onion and pickles into potato mixture.
Whisk mayonnaise, mustard, chives, black pepper, and egg yolks together until smooth. Gently mix mayonnaise mixture into potato mixture until evenly coated; refrigerate for 10 to 15 minutes.