Step 1: Marinate the Chicken : In a large bowl, whisk together olive oil, yogurt, lemon juice, garlic, oregano, cumin, paprika, salt, and pepper. Add the chicken and toss to coat evenly. Cover and refrigerate for at least 1 hour (up to 6 hours for best flavor).
Step 2: Prepare the Tzatziki Sauce : Grate cucumber, then squeeze out excess moisture using a clean kitchen towel. Combine Greek yogurt, cucumber, garlic, olive oil, lemon juice, and dill in a bowl. Mix well and season with salt and pepper. Chill until ready to serve — the flavors will deepen over time.
Step 3: Cook the Chicken : Heat a grill pan or skillet over medium-high heat. Add marinated chicken and cook for 5–6 minutes per side, until golden brown and fully cooked (internal temp: 165°F / 74°C). Let rest for 5 minutes, then slice thinly.
Step 4: Warm the Pitas : Lightly brush each pita with olive oil. Warm them on a dry skillet for about 30 seconds per side or in the oven at 350°F (175°C) for 5 minutes.
Step 5: Assemble the Gyro Wraps : Lay a warm pita flat on a plate. Spread 2 tablespoons of tzatziki sauce in the center. Add lettuce, tomato, cucumber, and red onion. Top with slices of grilled chicken. Sprinkle feta cheese if desired. Drizzle a bit more tzatziki or lemon juice on top. Fold the pita into a wrap or secure it with parchment paper.
Step 6: Serve : Serve warm with extra tzatziki sauce on the side, lemon wedges, and maybe a few Greek-style roasted potatoes or a side salad.