Preheat the oven to 400°F (200°C).
Place the pita breads on a large baking sheet and brush the edges lightly with olive oil.
Spread 1/4 cup of hummus evenly over the surface of each pita, leaving a small border for the crust.
Distribute the shredded chicken, red onion, and cherry tomatoes evenly across both pitas.
Sprinkle with dried oregano and crumbled feta cheese.
Bake in the preheated oven for 8 to 10 minutes until the pita edges are golden brown and the toppings are heated through.
Remove from the oven and top with the diced cucumber, kalamata olives, and fresh parsley.
Slice each pita into quarters and serve immediately.