Cut asparagus into 4cm lengths and separate tips and stalks. Cook tips in boiling, salted water for 1 minute. Drain and refresh under cold water. Set aside.
Melt butter in a saucepan on medium heat. Stir in asparagus stalks, leek and potato and cook, covered, for 10 minutes, until soft without colouring. Add stock with 3 1/2 cups water and bring to boil. Simmer for 8-10 minutes.
Puree in batches, using a blender or food processor. Reheat, add milk and season to taste. Sprinkle with chives, and serve with asparagus tips and crusty bread.