In a large bowl toss hearts of palm slices, oil, garlic, oregano, salt, and pepper. Marinate 20 minutes for flavors to blend.
Cut cherry tomatoes in half. To serve, spread out lettuce on a serving platter. For each hors d'oeuvre, skewer one heart of palm piece and and one tomato half on a toothpick. Arrange on platter; scatter olive halves over all.