In a large saucepan, cook the onion, celery, and garlic in hot butter over medium heat for 3 to 5 minutes or until just tender, but not brown. Stir in the chicken stock, parsnips, salt, black pepper, and bay leaf. Bring to boiling; reduce heat. Simmer, covered, for 25 to 30 minutes or until parsnips are very tender. Remove from heat. Cool slightly (do not drain). Remove bay leaf; discard.
Transfer half of the mixture to a food processor bowl or blender container. Cover and process or blend until nearly smooth. Repeat with remaining mixture. Return to same saucepan. Stir in the whipping cream. Cook and stir for 4 to 5 minutes or until heated through.
To serve, ladle soup into bowls. Top each serving with chives. Makes 6 cups (6 side-dish servings).