In a bowl, whisk together olive oil, red wine vinegar, minced garlic, dried oregano, ground cumin, smoked paprika, and a pinch of salt and pepper. Add chicken thighs and coat well. Cover and refrigerate for at least 1 hour.

In a mixing bowl, combine Greek yogurt, grated cucumber, minced garlic, olive oil, fresh dill, and lemon juice. Stir until smooth, then taste and adjust seasoning with salt. Cover and refrigerate until ready.

Preheat grill or grill pan over medium-high heat. Remove chicken from marinade and cook for about 5-7 minutes on each side until cooked through. Alternatively, bake in a preheated oven at 400°F for 20-25 minutes.

Warm pita bread in a dry skillet for about 1 minute on each side until soft and pliable. Keep covered until serving.

To assemble, lay a warm pita flat and top with grilled chicken, tzatziki sauce, cherry tomatoes, sliced red onion, lettuce, and crumbled feta cheese. Garnish with parsley if desired.

Serve the assembled gyros immediately while warm and fresh. Drizzle with extra olive oil if desired.