In a mixing bowl, whisk together the Greek yogurt, minced garlic, lemon juice, olive oil, dried oregano, ground cumin, and a generous pinch of salt and pepper. This will be your flavorful marinade.
Add the thinly sliced chicken breast to the marinade, ensuring that each slice is completely coated with the mixture. Cover the bowl with plastic wrap and refrigerate for at least 30 minutes.
Preheat either a grill or a skillet over medium-high heat, ensuring it is hot enough for a nice sear.
Remove the chicken from the marinade, allowing any excess to drip off. Grill the chicken slices for approximately 6-7 minutes on each side, or until they are fully cooked through and have a beautiful golden-brown color. After cooking, remove the chicken from heat, let it rest for a few minutes, then slice it into bite-sized pieces.
In a separate bowl, combine the diced cucumber, tomatoes, thinly sliced red onion, chopped parsley, and crumbled feta cheese. Toss gently to mix.
Take a soft pita bread and lay it flat. Spoon a generous portion of the grilled chicken onto the center, followed by the fresh vegetable-feta mixture.
Carefully fold the pita bread over the filling, encasing it securely. Serve immediately while still warm.
Notes
Serve with tzatziki and lemon wedges for added flavor.