Remove the lower third of the asparagus stems. Bring a large pot of salted water to a boil, add a teaspoon butter and the asparagus. Cook for 5-7 minutes, depending on how thick the stalks are, they should remain rather firm or al dente. Remove from the water and drain well.
In the meantime make the vinaigrette: whisk together the vinegar, oil, and mustard. Add salt and pepper to taste.
Sprinkle the asparagus with about half of the vinaigrette and rub the spears gently with the dressing. Let marinate for about 30 minutes.
In the meantime cook the potatoes in a large pot of salted water until tender.
Boil the eggs until hard. Leave to cool slightly, peel and chop the eggs finely. Keep a few whole slices for decoration purposes, if desired.
Chop the ham and the chives.
Arrange the asparagus stems and the potatoes on a platter. Top with the eggs, ham, and chives and sprinkle with the remaining vinaigrette.
Alternatively, slices the potatoes, cut the asparagus into shorter pieces, and mix everything with the dressing.