Easy prep for this recipe. Finely chop the onion. Trim, peel, and coarsely chop the celery root or if you are using celery, slice it thinly.
Peel the potatoes and cut them into 1-inch cubes.
Rinse, drain, and pat dry the canned chestnuts.
In a large saucepan, cook the onion in 1½ tablespoons of the butter over moderately low heat, stirring, until softened.
Add the celery root, potatoes, chestnuts, chicken broth, and enough water to just cover the mixture and simmer, covered, for 15-20 minutes or until the vegetables are very tender.
Drain the mixture while reserving the cooking liquid.
Force the vegetables through a food mill fitted with the medium disk or a ricer into a warm bowl and stir in the remaining 1½ tablespoons butter, salt and white pepper to taste, and enough of the reserved cooking liquid to achieve the desired consistency.
Transfer the puree to a serving dish and garnish with the celery leaves.