Place potatoes in large saucepan. Add enough cold water to cover potatoes. Bring to gentle boil on medium-high heat. Cook 8 to 10 minutes or until fork-tender. Drain. Let cool completely.
Reserve 1 tablespoon of the red onion. Mix mayonnaise, mustard, vinegar and OLD BAY in large bowl until well blended. Add potatoes, eggs and remaining red onion; toss to coat well. Cover.
Refrigerate at least 1 hour or until ready to serve. Sprinkle with chives and reserved 1 tablespoon red onion before serving. If desired, sprinkle with additional OLD BAY.