Make the marinade: In a bowl, whisk olive oil, lemon zest and juice, garlic, oregano, cumin, smoked paprika, salt, and pepper.
Marinate the chicken: Add chicken and toss to coat.
Cover and refrigerate for at least 30 minutes, preferably 2–8 hours. The longer it marinates, the more tender and flavorful it gets.
Prep the tzatziki: Mix yogurt, grated cucumber (squeezed dry), olive oil, lemon juice, dill, garlic, and salt. Adjust salt and lemon to taste.
Chill until serving.
Chop the veggies: Slice red onion, tomatoes, cucumber, and lettuce. Set aside.
Cook the chicken: Heat a large skillet over medium-high and add a drizzle of oil. Cook chicken pieces 4–6 minutes per side until browned and cooked through (165°F/74°C).
For grilling, cook over medium-high heat 4–5 minutes per side. Rest 5 minutes, then slice.
Warm the flatbreads: Heat gluten-free pitas in a dry skillet for 30–60 seconds per side or wrap in foil and warm in a 325°F (165°C) oven for 5–7 minutes. Soft, warm bread is key.
Assemble: Spread tzatziki over each flatbread.
Add sliced chicken, tomatoes, onion, cucumber, and lettuce. Sprinkle feta if using. Squeeze with a little lemon.
Serve: Fold and enjoy immediately while warm and juicy.