Place potato in a large saucepan, and cover with water. Bring to a boil. Reduce heat, and simmer 15 minutes or until tender. Drain. Cool; cover and chill. Stir in onion.
Combine mayonnaise, chopped fresh chives, fresh lemon juice, salt, and freshly ground black pepper in a small bowl, stirring with a whisk. Add mayonnaise mixture to potato mixture; toss gently to coat. Cover and refrigerate 4 hours or overnight. Sprinkle radishes over potato mixture just before serving.