Position knife blade in food processor bowl. Drop garlic through food chute with processor running; process 3 seconds or until garlic is minced. Add parsley, capers, and olives. Process 10 seconds or until finely minced. Transfer mixture to a small bowl. Stir in yogurt and next 3 ingredients. Cover and chill.
Place potatoes in a large saucepan; add water to cover. Bring to a boil; cover, reduce heat, and simmer 10 minutes. Add chicken; cover and cook 10 to 15 minutes or until potato is tender and chicken is done. Drain well, and let cool.
Cut potatoes into 1/2-inch-thick slices. Cut chicken into 1/2-inch cubes. Place potato and chicken in a large bowl. Add tomato; toss lightly. Pour yogurt mixture over potato mixture, and toss lightly. Serve immediately, or cover and chill up to 8 hours.
To serve, place 2 lettuce leaves on each of 4 plates. Spoon potato mixture evenly over lettuce.