In a large saucepan, combine potatoes, celery root and garlic cloves. Pour over enough water to cover and set pan over high heat. Bring to a boil, reduce heat to medium and simmer 10 minutes, until potatoes are fork-tender.
Drain and transfer potatoes, celery root and garlic to a large bowl. Add buttermilk and olive oil and mash until smooth (or lumpy, whatever you like!). Fold in chives. Season, to taste, with salt and black pepper.