In a stock pot, saute onion in butter until yellow and soft. Add chicken stock, carrots, celery tops and potatoes. Stir in salt and white pepper. Bring to a boil and then reduce heat and cook until vegetables are tender enough to easily pierce with a fork.
Remove carrots and celery tops and discard. Add evaporated milk and heat through.
Using a food processor or blender, puree soup in small batches. Return to stock pot and keep over low heat until ready to serve, making sure soup does not scorch if not serving immediately. Garnish with chives and serve.