In a medium bowl, combine the olive oil, minced garlic, dried oregano, ground cumin, smoked paprika, sea salt, and freshly ground black pepper to form a fragrant marinade.
Place the chicken thighs in the marinade, ensuring each piece is well-coated. Cover the bowl with plastic wrap and refrigerate for at least 30 minutes, but up to 2 hours for a deeper flavor infusion.
Preheat your grill or grill pan to medium-high heat. Once hot, remove the chicken from the marinade, allowing excess to drip off. Grill the chicken for approximately 5-7 minutes on each side, or until the chicken is fully cooked, with an internal temperature reaching 165°F (75°C).
After cooking, transfer the chicken to a cutting board and let it rest for 5 minutes before slicing into thin strips.
While the chicken rests, warm the pita breads on the grill for about 1 minute on each side until they become soft and pliable, making them easier to wrap.
To assemble each wrap, start with a handful of shredded romaine lettuce in the center of the warm pita.
Layer on the sliced grilled chicken, diced cucumbers, juicy tomatoes, and thin slices of red onion for a vibrant crunch.
Generously drizzle tzatziki sauce over the top and add fresh dill sprigs for an aromatic finish, if desired.
Carefully fold in the sides of the pita, then roll it tightly from the bottom to encase all the delicious fillings inside.
Serve your Greek Chicken Gyro Wraps immediately, accompanied by additional tzatziki sauce on the side for dipping.
Notes
For a deeper flavor, marinate the chicken for up to 2 hours.