In a medium pot, cover potatoes with water. Add salt and and bring to a simmer. Simmer gently until just fork tender, about 15-17 minutes, being especially careful not to overcook, keeping them slightly al dente.
While the potatoes are simmering, make the dressing. In a small bowl, mix the chives, shallot, olive oil, capers, mustard, salt and pepper together and set aside.
Strain and gently rinse the potatoes with cold water until cooled. Drain well.
Place in a bowl and very gently toss with the dressing.