In a large resealable bag or shallow baking dish, combine the olive oil, lemon juice, red wine vinegar, garlic, oregano, cumin, smoked paprika, and cinnamon. Add the chicken thighs and turn to coat them evenly. Cover and refrigerate for at least 30 minutes, or up to 4 hours.
Preheat your grill or grill pan to medium-high heat.
Remove the chicken from the marinade, allowing any excess to drip off. Grill the chicken for 5-7 minutes per side, or until it reaches an internal temperature of 165°F. Transfer the grilled chicken to a cutting board and let it rest for 5 minutes before slicing.
In a medium bowl, combine the Greek yogurt, grated cucumber, and chopped dill. Season with salt and pepper to taste. Cover and refrigerate for at least 30 minutes.
To assemble the gyros, place a few slices of the grilled chicken in the center of a warm pita bread. Top with a generous amount of the tzatziki sauce, followed by the diced tomatoes, shredded lettuce, and diced red onion.
Serve the chicken gyros immediately, with lemon wedges on the side.