01 - In a mixing bowl, whisk together olive oil, lemon juice, minced garlic, dried oregano, ground cumin, smoked paprika, salt, and black pepper until well combined.
02 - Add the chicken to the marinade, tossing to coat evenly. Cover and refrigerate for at least 20 minutes, or up to overnight for deeper flavor penetration.
03 - Preheat a grill or grill pan over medium-high heat. Remove chicken from the marinade and grill for 5 to 6 minutes per side, until fully cooked through with a nicely charred exterior. Let the chicken rest for 5 minutes, then slice thinly against the grain.
04 - In a bowl, combine Greek yogurt, mayonnaise, finely minced garlic, lemon juice, salt, black pepper, and fresh herbs. Stir until smooth and creamy. Adjust seasoning to taste.
05 - Place pita breads on the grill or in a dry skillet over medium heat for about 30 seconds per side, until warm and pliable.
06 - Layer sliced chicken, shredded lettuce, tomato slices, cucumber, and red onion onto each warmed pita. Drizzle generously with the creamy garlic sauce and sprinkle with fresh parsley if desired. Fold or roll the gyros and serve immediately.