In a large bowl, whisk together the cumin, garlic ,red chilliy powder, and oil. Add the diced chicken pieces and toss well to coat.
Heat a large skillet over medium-high heat. Once the pan is hot, add the chicken in a single layer and allow it cook for 2 minutes undisturbed. Continue to saute the chicken until cooked through, another 2-3 minutes.
Meanwhile, make the sauce by whisking together the Greek yogurt, oregano and salt to taste.
Assemble the pita sandwiches by spreading 2 tbsp yogurt sauce over each pita, then topping with cooked chicken, cucumber and tomato slices, and topping with crumbled Feta cheese.