Scrub potatoes, but do not peel.
Place the potatoes in a saucepan, cover with water and cook, covered, just until tender, about 10 to 15 minutes.
Meanwhile, in serving bowl, whisk together the oil, vinegar and mustard.
Stir the pitted, sliced olives into dressing.
Add the celery, red pepper, smoked chicken and parsley. Toss.
When potatoes are cooked, drain and cut into bite-sized pieces.
Add warm potatoes to salad.
Season mixture with salt and pepper; toss to blend.
Serve on lettuce leaves with tomato wedges.
Makes 3 main course servings.