In a bowl, mix together the olive oil, minced garlic, dried oregano, ground cumin, paprika, salt, and pepper to create a marinade.
Add the chicken thighs to the marinade, ensuring they are fully coated. Cover and let marinate in the refrigerator for at least 30 minutes (or up to 2 hours for more flavor).
Preheat a grill or a grill pan over medium-high heat. Remove the chicken from the marinade and grill for about 5-7 minutes on each side, or until fully cooked and internal temperature reaches 165°F (75°C).
Once cooked, let the chicken rest for a few minutes before slicing it into thin strips.
In the meantime, warm the pita breads on the grill for about 1 minute on each side until they are soft and pliable.
To assemble the wraps, start by adding a handful of shredded romaine lettuce to the center of each pita.
Layer on the sliced chicken, diced cucumbers, diced tomatoes, and red onion.
Drizzle with tzatziki sauce and sprinkle fresh dill on top if desired.
Fold the sides of the pita up and roll it tightly, enclosing the fillings.
Serve immediately, with additional tzatziki on the side for dipping.
Notes
For extra flavor, marinate the chicken for up to 2 hours.