In a bowl, combine olive oil, dried oregano, garlic powder, paprika, salt, and pepper. Add the chicken breasts, ensuring they are fully coated in the marinade. Cover and refrigerate for at least 30 minutes, or up to 2 hours for deeper flavor.
Preheat a grill pan or outdoor grill over medium-high heat. Remove the chicken from the marinade, allowing excess to drip off. Grill the chicken for about 6-7 minutes per side, or until fully cooked and internal temperature reaches 165°F (75°C). Remove from the grill and let it rest for 5 minutes.
Once rested, slice the grilled chicken into thin strips.
Warm the pita breads slightly in a skillet or grill for a few seconds on each side to make them pliable. Spread a generous spoonful of tzatziki sauce on each pita.
Add a layer of shredded romaine lettuce, diced tomatoes, cucumber slices, red onion, and then top with the sliced chicken.
Fold the sides of the pita over the filling and then roll it tightly from the bottom to enclose the fillings.
Cut the wrap in half diagonally and serve with extra tzatziki sauce on the side for dipping. Garnish with fresh parsley if desired.
Notes
For best flavor, marinate the chicken for up to 2 hours.