Add the minced garlic, vinegar, lemon juice, olive oil, Greek yogurt, oregano, salt, and black pepper to a large resealable bag or covered container. Mix until combined.
Add the chicken thighs and coat them thoroughly with the marinade. Refrigerate for at least 2 hours, preferably 3–12 hours. Do not marinate for longer than 24 hours.
To prepare the tzatziki, cut the cucumbers in half lengthwise and scrape out the watery seeds with a teaspoon. Coarsely grate the cucumber.
Wrap the grated cucumber in a clean kitchen towel or several layers of paper towel and squeeze firmly to remove as much excess moisture as possible.
Transfer the cucumber to a bowl. Add Greek yogurt, lemon juice, olive oil, garlic, salt, and black pepper. Stir well and refrigerate for at least 20 minutes so the flavors can develop.
For the salad, combine the diced tomatoes, cucumbers, red onion, and parsley in a bowl. Season lightly with salt and pepper.
Preheat an outdoor grill over medium-high heat and lightly oil the grates. Alternatively, heat about 1 tablespoon of oil in a large skillet over medium-high heat.
Remove the chicken from the marinade, allowing the excess marinade to drip away. Cook for approximately 2–3 minutes per side, adjusting the cooking time according to the thickness of the thighs. Cook until golden and the thickest part reaches a safe internal temperature of 165°F (74°C).
Transfer the cooked chicken to a plate and loosely cover it. Rest for 5 minutes, then slice into strips or bite-sized pieces.
Warm the pita breads until soft and flexible. To assemble this Greek Chicken Gyros recipe, add salad down the center of each pita, followed by sliced chicken and a generous spoonful of tzatziki.
Fold or roll the pita around the filling and serve immediately.