01 - In a mixing bowl, combine olive oil, lemon juice, minced garlic, ground cumin, smoked paprika, coriander, dried oregano, cayenne pepper, salt, and black pepper. Add the sliced chicken and toss thoroughly to coat. Allow to 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, chopped 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 pieces are cooked through and lightly charred on the edges. 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 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 with the cooked chicken and drizzle generously with the prepared yogurt sauce.
06 - Serve the filled pitas immediately while warm. Accompany with lemon wedges on the side if desired.