Preheat oven to 400°F. Line a baking sheet with foil.
Split each pita in half horizontally into rounds. Coat cut sides of pitas with cooking spray. Cut each pita half into 8 wedges. Arrange half of wedges, cut side up on the baking sheet. Bake for 7-8 minutes or until browned; remove from pan. Let cool.
Combine oil, vinegar, and pepper in a medium bowl, stirring with a whisk. Add lettuce, tomatoes, cucumber, and olives; toss to coat.
Arrange all pita chips on foil-lined baking sheet so they overlap. Top with chicken, mozzarella, and feta. Bake at for 3-4 minutes or until cheese melts. Top with lettuce mixture and oregano.