In a bowl, whisk together olive oil, lemon juice, garlic, oregano, cumin, paprika, salt, and pepper.
Add the chicken, ensuring it's well-coated. Cover and let it marinate in the refrigerator for at least 30 minutes (or up to 4 hours for deeper flavor).
Grill the Chicken
Preheat your grill or grill pan to medium-high heat.
Remove chicken from the marinade and cook for 6-8 minutes per side, or until fully cooked (internal temperature of 165°F). Let it rest for 5 minutes, then slice into strips.
Prepare the Wrap Components
Warm the pita bread on the grill or in a dry skillet for about 1 minute per side.
Lay out the pita and spread a generous dollop of tzatziki sauce in the center.
Assemble the Wraps
Layer lettuce, tomatoes, cucumbers, and red onion on the pita.
Add sliced chicken and sprinkle feta cheese over the top.
Wrap and Serve
Fold the sides of the pita and roll it into a wrap. Secure with foil or a toothpick if needed. Serve immediately, with extra tzatziki on the side for dipping.