In a large saucepan cover the potato pieces with cold salted water and set over medium heat. Bring to a boil, then lower the heat slightly and cook uncovered, stirring a few times, until the potatoes are just tender, about 12 minutes. Drain and transfer to a large bowl. Pour the pickle juice over the hot potatoes, stir gently and cool to room temperature.
Place the diced red onion in a small bowl and cover with ice water. Let sit 20 minutes to reduce the acidity. Drain and squeeze out the excess moisture with a paper towel. Add to the potatoes.
In a medium bowl stir together the mayonnaise, sour cream, horseradish mustard, salt, pepper, pickles and chives. Pour this mixture over the potatoes and toss gently. Add the eggs and toss again. Spoon into a serving container. The salad can be prepared up to 1 day ahead. Refrigerate, covered.
Sprinkle salad with paprika at serving time.