Mix the marinade: In a large bowl, whisk together 1/2 cup of the Greek yogurt, 3 tablespoons of the lemon juice, 2 tablespoons of the olive oil, the red wine vinegar, 4 cloves of the minced garlic, the oregano, smoked paprika, cumin, 1 1/2 teaspoons of the salt, and the black pepper.

Marinate the chicken: Add the chicken thighs and turn to coat every piece. Cover and refrigerate for at least 30 minutes, or up to 24 hours for deeper flavor.

Make the tzatziki: Wrap the grated cucumber in a clean kitchen towel and wring it out hard over the sink until it stops dripping. Stir it together with the remaining 1 1/2 cups yogurt, the remaining clove of garlic, the remaining 1 tablespoon lemon juice, 1 tablespoon of the olive oil, the dill, and the remaining 1/2 teaspoon salt. Cover and chill until you're ready to serve.

Cook the chicken: Heat the last 1 tablespoon of olive oil in a large skillet over medium-high heat. Lift the thighs out of the marinade, letting the excess drip off, and cook in a single layer for 5 to 6 minutes per side, until deeply browned and a thermometer in the thickest part reads 165°F. Work in two batches if your pan is crowded.

Rest and slice: Move the chicken to a cutting board and let it rest for 5 minutes, then slice it across the grain into thin strips. Resting keeps the juices in the meat instead of on the board.

Warm the pita: Wipe out the skillet and warm each pita over medium heat for about 30 seconds per side, until soft and pliable with a few blistered spots.

Build the gyros: Spread a spoonful of tzatziki down the middle of each warm pita. Top with sliced chicken, romaine, tomato, and red onion, then add another spoonful of tzatziki and fold. Serve the extra sauce on the side.