In a bowl, mix together the olive oil, lemon juice, smoked paprika, cumin, minced garlic, turmeric, coriander, salt, black pepper, onion powder, cinnamon, and red pepper flakes. Add the chicken breast, ensuring it is evenly coated. Marinate for 20 minutes.
While the chicken marinades, make the tzatziki sauce. In a blender, combine the garlic, fresh dill, Greek yogurt, and lemon juice. Blend until smooth. Taste and adjust seasoning with salt and black pepper as needed. Refrigerate until serving.
Heat a grill or griddle pan over medium heat.
Remove the chicken from the marinade, letting any excess drip off. Place the chicken on the grill and cook for about 6 minutes per side, flipping once, until it reaches an internal temperature of 165°F (74°C). Use a meat thermometer to confirm doneness. Once cooked, transfer to a plate and let it rest before chopping into bite-sized pieces.
While the chicken rests, warm the pita bread on the grill or griddle pan, heating each side for about 30 seconds until soft and slightly charred.
Assemble the gyro by layering the pita bread with romaine lettuce, grilled chicken, red onion, grape tomatoes, olives, feta cheese, and tzatziki sauce.
In a pitcher, mix together the fresh lemon juice, water, and sugar. Stir until the sugar dissolves. Serve over ice if desired.
Serve the gyro with pita carrots, hummus, pickle spears, and homemade lemonade. Enjoy!