In a bowl, combine olive oil, lemon juice, garlic, oregano, cumin, salt, and pepper. Add chicken and marinate for at least 1 hour.
Preheat grill or skillet over medium-high heat. Cook chicken slices 4–5 minutes per side until cooked through and slightly charred.
For tzatziki, mix yogurt, grated cucumber, garlic, lemon juice, dill, salt, and pepper in a bowl.
Warm pita breads. Fill each with chicken, tzatziki, tomatoes, onion, and parsley.
Serve immediately.
Nutrition (per gyro, serves 4)
Calories: 420
Protein: 35g
Fat: 16g
Carbohydrates: 30g
Fiber: 3g