For dressing, shake together oil, vinegar, salt, pepper, chives, and parsley; chill.
Cook unpeeled potatoes in boiling, salted water 20 minutes, or until tender; cool immediately under cold water; peel and slice.
Pour over just enough dressing to coat slices, mix lightly.
Cover; chill at least 2 hours.
Cut offends of beans and cut into 1 1/2-inch lengths; cook in boiling, salted water about 15 minutes or until crisp-tender; drain and cool immediately with cold water.
Drain well again, then turn into a bowl and coat lightly with dressing.
Cover and chill at least 2 hours.
Select a rimmed platter or large, shallow bowl and mound potato salad down the center.
Arrange marinated green beans on each side.
Peel tomatoes and cut in wedges.
Quarter the hard-cooked eggs and alternate the egg quarters and tomato wedges beside the green beans.
Criss-cross the anchovy fillets across the top of the potatoes.
Garnish with olives and sprinkle with capers.