Marinate the Chicken: In a large bowl, combine chicken breasts, olive oil, lemon juice, minced garlic, oregano, salt, and pepper. Mix well and cover with plastic wrap. Marinate in the refrigerator for at least 30 minutes.

Cook the Chicken: Heat a grill pan over medium-high heat. Cook marinated chicken for about 6-8 minutes on each side until browned and cooked through (internal temperature 165°F). Let rest before slicing.

Prepare the Tzatziki Sauce: Mix Greek yogurt, grated cucumber, minced garlic, lemon juice, salt, dill, and a splash of olive oil in a bowl. Chill in the refrigerator for about 10 minutes before serving.

Assemble the Gyros: Warm pita bread until pliable. Slice cooked chicken and place in the center of each pita. Top with sliced tomatoes, red onion, and tzatziki sauce.

Serve and Enjoy: Fold pita over fillings and serve immediately. Optionally garnish with fresh parsley or additional vegetables.