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 for 8 to 10 minutes, or until potatoes are fork-tender.
Drain and transfer potatoes, celery root and garlic to a large bowl. Add 1/2 cup buttermilk and olive oil and mash or process until smooth (or lumpy, whatever you like!). Add more buttermilk if you want smoother potatoes. Fold in chives. Season to taste with salt and black pepper.