Melt margarine in a large Dutch oven over medium-high heat. Add leek and shallots; sauté 4 minutes. Add turnips; sauté 2 minutes. Stir in water and broth; bring to a boil. Reduce heat; simmer 30 minutes or until turnips are tender.
Place one-third of turnip mixture in a blender; process until smooth. Pour puréed mixture into a large bowl; repeat procedure with remaining turnip mixture. Return turnip purée to pan; stir in milk and pepper. Cook until thoroughly heated. Ladle into soup bowls; garnish with fresh chives, if desired.