01 - In a 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. Let marinate for at least 15 minutes at room temperature, or refrigerate 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 large skillet over medium-high heat. Add the marinated chicken in an even layer and cook for 6 to 8 minutes, stirring occasionally, until the chicken is cooked through and develops a light char. Remove from heat and set aside.
04 - Briefly warm each pita bread in a dry skillet over medium heat for about 30 seconds per side, or microwave for 15 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 the assembled pitas immediately while the chicken is still warm. Garnish with extra lemon wedges on the side if desired.