Place potatoes and celery root in a medium saucepan. Add cold water to cover by 2 inches, and bring to a boil. Reduce heat, and simmer 10 minutes. Add apple, and simmer 5 minutes, or until potato and celery root are tender. Drain, and return to pan. Add buttermilk, butter, salt, and pepper, and mash until smooth with a whisk or potato masher. (If you like a smoother texture, puree the mixture with an immersion blender or transfer it to a blender or food processor.) Stir in chives.