1. In a mixing bowl, combine Greek yogurt, minced garlic, olive oil, lemon juice, 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 a grill pan over medium-high heat. Grill the marinated chicken breasts for 6-7 minutes on each side, or until fully cooked.
4. Let the chicken rest for a few minutes, then slice into strips.
5. Warm the pita bread in the oven or on a skillet.
6. Assemble the sandwiches by placing chicken strips, diced cucumber, tomato, and sliced red onion inside each pita.
7. Serve immediately and enjoy!