Peel onion and garlic and chop coarsely. Clean, wash and cut the cucumber into large pieces. Wash chives, shake dry and cut into small rolls. Coarsely crush ice cubes.
Blend everything together with the cream cheese in a blender or with a hand blender. Season to taste with salt, pepper and Worcester sauce. Arrange in glasses and garnish with cucumber slices if desired. Serve with grissini sticks as a starter.