Put potatoes in a large saucepan with water to cover. Cover pan and bring to a boil over high heat, then reduce heat and simmer until potatoes are tender when pierced, 10 to 12 minutes. Drain, then rinse occasionally with cold water until room temperature.
Meanwhile, put lettuce, chervil, parsley, marjoram, and tarragon in a large bowl and chicken in a second large bowl. In a small bowl, whisk yogurt, chives, oil, salt, and pepper.
Slice potatoes crosswise, add to chicken, and toss with about 2/3 cup dressing. Toss greens and arrange on plates. Spoon chicken mixture on top. Grind pepper generously over each serving. Serve with remaining dressing and more salt to add to taste.