Place potatoes in a medium pot and cover with lightly salted water. Bring to a boil, and cook until fork-tender, about 15 minutes. Meanwhile, make vinaigrette. Drain potatoes and place in a large bowl; add vinaigrette and toss. Using a slotted spoon, divide dressed potatoes among four plates, leaving plenty of vinaigrette in bowl.
Place green beans in pot and cover with lightly salted water. Bring to a boil and cook until tender but crisp; drain and place in bowl with vinaigrette. Toss. Using tongs, divide among plates, arranging atop potatoes. Toss arugula in remaining vinaigrette, and divide among plates.
Add tomatoes and 1 tablespoon minced chives to bowl. Toss and divide among plates, arranging on top of arugula along with herring. Garnish plates with cheese, pickles and chives. Serve.