Remove and discard roots, tough outer leaves, and tops from leeks; wash thoroughly, and thinly slice.
Sauté leeks and onion in butter in a large saucepan; add chicken broth, potatoes, and salt. Cook, uncovered, over medium heat 20 minutes or until potatoes are tender. Process 2 cups potato mixture in container of an electric blender until smooth; repeat procedure with remaining potato mixture.
Pour pureed potato mixture into a large bowl; add milk, half-and- half, whipping cream, and sour cream, stirring with a wire whisk until well blended and smooth. Cool mixture to room temperature; cover and chill thoroughly.
Serve Vichyssoise in chilled soup bowls; garnish with chives, if desired.