1. In a mixing bowl, combine Greek yogurt, olive oil, garlic, lemon juice, oregano, salt, and black pepper to make the marinade.
2. Add the chicken cubes to the marinade, mix well, and let it marinate for at least 30 minutes.
3. Preheat the grill to medium-high heat.
4. Thread the marinated chicken onto skewers.
5. Grill the chicken skewers for about 10-15 minutes, turning occasionally, until fully cooked.
6. Warm the pita bread on the grill for a minute on each side.
7. Assemble the gyros by placing grilled chicken, tzatziki sauce, tomatoes, red onions, and lettuce on the pita bread.
8. Roll up the pita bread and serve immediately.