In a bowl, whisk together olive oil, Greek yogurt, minced garlic, oregano, cumin, smoked paprika, salt, and pepper to create a marinade.
Add the chicken thighs into the bowl, ensuring they're well coated. Cover and marinate in the refrigerator for at least 30 minutes, or up to 2 hours for more flavor.
Preheat your grill or grill pan over medium-high heat.
Remove the chicken from the marinade and grill for about 6-7 minutes on each side, or until fully cooked (internal temperature should reach 165°F).
Once grilled, let the chicken rest for a few minutes before slicing it into thin strips.
Warm the pita breads on the grill for about 1 minute each, just until they are soft and warm.
Assemble the gyros by placing a generous amount of grilled chicken strips on each pita.
Top with diced tomatoes, cucumber, sliced red onion, and shredded lettuce.
Drizzle with tzatziki sauce before wrapping the pita around the filling.