Place the potatoes in a large pot; cover with water by 2 inches. Season generously with salt and bring to a boil. Reduce to a simmer and cook until the potatoes are tender, about 20 minutes. Drain the potatoes; let cool 15 to 20 minutes.
Whisk the olive oil, vinegar, 1 teaspoon salt and a few grinds of pepper in a medium bowl; stir in the olives and diced celery. Halve the potatoes and transfer to a shallow bowl. Scatter the tomatoes over the potatoes, then drizzle with the vinaigrette. Scatter the celery leaves, basil and chives over the salad and season with salt and pepper.
Photograph by Ryan Liebe
Recipe courtesy of Food Network Magazine