In a bowl, combine yogurt, lemon juice, red wine vinegar, olive oil, minced garlic, cumin, oregano, dried thyme, paprika, cinnamon, salt, pepper, and red chili flakes. Whisk until smooth and well combined. Add the chicken thigh strips and toss until every piece is evenly coated. Transfer to a sealed container or zip-top bag and refrigerate for at least 1 hour, ideally 2-4 hours, to allow the flavors to penetrate the meat and tenderize it. I find that marinating overnight gives the most authentic, deeply flavored result, but even 1 hour makes a noticeable difference.
Preheat your oven to 425°F. Remove the marinated chicken from the refrigerator and arrange the strips in a single layer on a baking rack set over a sheet pan (the rack allows air to circulate underneath for even cooking). Bake for 15-18 minutes until the chicken is cooked through and the exterior begins to brown. The chicken should reach an internal temperature of 165°F and show light caramelization on the edges.
Switch your oven to broil and place the baking sheet on the upper rack, about 4-6 inches from the heating element. Broil for 2-3 minutes until the chicken develops crispy, charred edges that mimic the texture of traditional rotisserie-cooked gyro meat. Watch carefully to prevent burning—the chicken should have light golden-brown spots and slight char. I like this step because it gives you that authentic crust without needing specialized equipment.
While the chicken broils or immediately after it finishes, warm the pita breads. You can place them directly on a stovetop burner over low-medium heat for 15-20 seconds per side, or wrap them in a damp paper towel and microwave for 20-30 seconds until they're soft and pliable. Warm pitas are essential—they hold the fillings better and create the authentic gyro experience.
Lay each warm pita flat on a work surface. Spread about 2 tablespoons of tzatziki down the center of each pita, then layer the crispy broiled chicken strips on top. Add a small handful of thinly sliced red onion half-moons and a generous spoonful of diced tomatoes to each gyro. Fold the pita in half or wrap it loosely around the fillings, and serve immediately while everything is still warm.