Step 1

Bring milk, water, and salt just to boil in heavy large saucepan over high heat. Add celery root cubes, potato cubes, and onion quarters; bring to boil. Reduce heat to medium and simmer until vegetables are tender, about 30 minutes. Drain, discarding cooking liquid.

Step 2

Combine vegetables and butter in processor and puree until smooth. Season to taste with salt and white pepper. Do ahead Celery root puree can be made 1 day ahead. Cover and chill. Rewarm in microwave before serving.

Step 3

Transfer celery root puree to bowl. Sprinkle with chopped fresh chives and serve.