In a large saucepan, cover the potatoes with 1 inch of water and add 1 tablespoon of salt. Cover with a lid and bring to a boil, then uncover, reduce the heat and simmer until the potatoes are easily pierced with a knife, about 15 minutes. Drain and let cool slightly, then cut into 1/2-inch chunks, slip the skins off and place the potatoes in a large nonreactive (stainless-steel, glass or plastic) bowl.
In a small bowl, whisk together the olive oil, vinegar, olives and onion. Season to taste with salt and pepper. Add the olive vinaigrette and the parsley to the potatoes and toss well. Serve warm or at room temperature.