In a medium bowl, combine chicken breast pieces with olive oil, lemon juice, garlic, oregano, salt, and pepper. Cover and let marinate for at least 30 minutes.

Heat a grill pan over medium-high heat and cook the marinated chicken for 6–8 minutes on each side until cooked through. Let it rest, then slice thinly.

Prepare the tzatziki by mixing yogurt, grated cucumber, garlic, lemon juice, salt, dill, and olive oil in a bowl. Refrigerate for 10 minutes.

Warm pita bread for about 30 seconds, then layer with sliced chicken, tzatziki, cherry tomatoes, red onion, and any additional toppings.

Serve garnished with parsley and enjoy with Greek salad or roasted vegetables.