1. In a mixing bowl, combine Greek yogurt, olive oil, lemon juice, minced garlic, dried oregano, salt, and black pepper. Mix well.
2. Add chicken breasts to the marinade, ensuring they are well coated. Cover and refrigerate for at least 30 minutes.
3. Preheat the grill to medium-high heat. Grill the marinated chicken breasts for about 6-7 minutes on each side or until fully cooked.
4. Remove the chicken from the grill and let it rest for a few minutes before slicing it into thin strips.
5. Warm the pita bread on the grill for about 1-2 minutes on each side.
6. Assemble the sandwiches by placing sliced chicken, diced cucumber, diced tomato, thinly sliced red onion, and crumbled feta cheese inside the warm pita bread.
7. Serve immediately and enjoy!