In a mixing bowl, combine Greek yogurt, olive oil, minced garlic, lemon juice, oregano, salt, and black pepper. Mix well.
Add chicken strips to the marinade, ensuring they are well coated. Cover and refrigerate for at least 1 hour.
Preheat the grill to medium-high heat. Grill the marinated chicken strips for about 5-7 minutes on each side, or until fully cooked.
Warm the pita bread on the grill for about 1-2 minutes.
Assemble the gyros by placing grilled chicken strips on the pita bread, and topping with sliced tomatoes, red onions, and tzatziki sauce.
Serve immediately and enjoy!