Prepare the marinade by mixing olive oil, lemon juice, minced garlic, oregano, salt, and black pepper in a bowl.
Cut the chicken breast into strips and marinate in the mixture for at least 30 minutes.
Preheat your grill or skillet over medium-high heat.
Cook the marinated chicken strips for about 5-7 minutes on each side until fully cooked.
Warm the pita breads on the grill for about a minute until soft and pliable.
Assemble the gyros by placing chicken strips in pita, topping with tzatziki, lettuce, tomatoes, and red onion.
Serve immediately while warm.