How to Make It
Put the potatoes in a medium saucepan of salted water. Bring to a boil, reduce the heat, and simmer until just tender, about 12 minutes. Drain the potatoes and let cool.
In a large nonstick frying pan, heat 1 tablespoon of the oil over moderate heat. Season the chicken with 1/4 teaspoon each of the salt and pepper. Cook the breasts until browned and just done, about 5 minutes per side. Remove the chicken from the pan and let it cool. Cut into 1/2-inch chunks.
In a large glass or stainless-steel bowl, whisk together the yogurt, mayonnaise, mustard, lime juice, and the remaining 1 1/4 teaspoons salt and 1/4 teaspoon pepper. Add the potatoes, chicken, carrots, cucumbers, celery, peas, onion, olives, parsley, and basil and toss.