In a large bowl, combine the Greek yogurt, olive oil, lemon juice, lemon zest, garlic, oregano, salt, black pepper, and paprika. Stir until smooth and evenly blended. The mixture should smell strongly of lemon, garlic, and oregano before the chicken ever touches the pan.
Add the whole chicken thighs and turn them until every piece is well coated. Cover and refrigerate for at least 30 minutes or up to about 8 hours. You don’t need an overnight marinade here; the lemon juice is acidic, and an excessively long soak can eventually change the surface texture of the chicken.
Coarsely grate half of an English cucumber. Gather the grated cucumber in a clean kitchen towel and squeeze firmly over the sink until you remove as much liquid as possible. Don’t skip the squeezing. Cucumber is mostly water, and leaving all of that moisture behind turns thick tzatziki into something closer to cucumber soup.
Combine the squeezed cucumber with Greek yogurt, olive oil, lemon juice, garlic, dill, salt, and a few grinds of black pepper. Taste and adjust the salt or lemon if needed, then refrigerate while the chicken cooks. Even 20–30 minutes in the refrigerator gives the garlic and dill time to settle into the yogurt.
Heat a large skillet or grill pan over medium-high heat. If you’re using an outdoor grill, preheat it to medium-high and clean the grates well. Remove the chicken from the marinade and let the excess drip away. You want a coating left on the thighs, but not thick blobs of marinade that will burn before the meat cooks.
Arrange the thighs in the hot pan without overlapping them. Cook for about 5–7 minutes on the first side, leaving them mostly undisturbed until you see browned, lightly charred patches. Flip and cook for another 4–6 minutes, depending on thickness. The chicken should reach at least 165°F (74°C) at its thickest point. Pro tip: Resist the temptation to cut the chicken into strips before cooking. Whole thighs lose moisture more slowly and are easier to brown without overcooking, which gives you juicier gyro meat after slicing.
Transfer the cooked chicken to a cutting board and leave it alone for 5 minutes. This small pause is worth keeping. Slicing the chicken immediately sends more juice onto the cutting board; resting gives that moisture time to redistribute before the knife goes through it.
While the chicken rests, warm the pita in a dry skillet for about 20–30 seconds per side, or briefly heat them on the grill. The goal isn’t to toast them crisp. You just want them warm, soft, and flexible enough to fold around the filling without tearing.
Cut the rested chicken thighs across the grain into thin strips. Spoon any juices left on the cutting board back over the sliced chicken rather than leaving that flavor behind.
Lay out a warm pita and spread a generous spoonful of tzatziki through the center. Add sliced chicken, tomato, cucumber, red onion, and lettuce if using. Finish with another small spoonful of tzatziki and a squeeze of lemon. Fold the pita around the filling and serve immediately.