01 - In a large mixing bowl, combine olive oil, lemon juice, minced garlic, cumin, smoked paprika, coriander, oregano, cayenne pepper, salt, and black pepper. Add the sliced chicken and toss thoroughly to coat. Cover and refrigerate for at least 15 minutes, or up to 8 hours for deeper flavor penetration.
02 - In a small bowl, whisk together the Greek yogurt, lemon juice, fresh dill, grated garlic, and season with salt and pepper to taste. Cover and refrigerate until ready to serve.
03 - Heat a grill pan or skillet over medium-high heat. Remove the chicken from the marinade and cook for 6 to 8 minutes, stirring occasionally, until the chicken is cooked through with a slightly charred exterior and reaches an internal temperature of 165°F. Remove from heat and set aside.
04 - Warm each pita bread briefly in a dry skillet over medium heat for about 30 seconds per side, or microwave for 15 to 20 seconds until pliable.
05 - Open each warm pita and layer with shredded romaine lettuce, diced cucumber, halved cherry tomatoes, and sliced red onion. Top generously with the cooked chicken and drizzle with the prepared yogurt sauce.
06 - Serve immediately while warm. Garnish with extra lemon wedges on the side if desired.