In a small bowl, whisk together the vinegar and mustard. Whisk in the oil. Season to taste with salt and pepper. Set aside.

In a large saucepan, combine the potatoes with water to cover and a generous pinch of salt. Bring to a boil over high heat, reduce the heat to medium, and cook for 8 minutes. Add the green beans and continue to cook until the potatoes are tender when pierced with the tip of a knife and the green beans are crisp-tender, 2-3 minutes longer. Drain the potatoes and green beans. Let cool slightly. Slice the potatoes and place in a bowl. Add the beans and 3 tablespoons of the vinaigrette and toss to coat.

Line a platter or individual plates with the lettuce leaves. Arrange the chicken, potatoes, green beans, tomatoes and olives on the lettuce. Sprinkle with the onion slices and basil.