In a large zip-top bag or bowl, combine the garlic, vinegar, lemon juice, olive oil, Greek yogurt, oregano, salt, and black pepper.
Add the chicken thighs and coat them evenly in the marinade.
Refrigerate for at least 2 hours, preferably 12 hours for the best flavor.
Prepare the tzatziki by halving the cucumbers lengthwise and removing the seeds.
Grate the cucumber, wrap it in a clean towel, and squeeze out as much moisture as possible.
Mix the grated cucumber with Greek yogurt, lemon juice, olive oil, garlic, salt, and pepper. Refrigerate for at least 20 minutes.
Combine the tomatoes, cucumbers, onion, parsley, salt, and pepper to make the salad.
Heat an outdoor grill or a skillet over medium-high heat and lightly oil the surface.
Remove the chicken from the marinade and cook for 2–3 minutes per side, or until golden brown and fully cooked.
Rest the chicken for 5 minutes before slicing.
Warm the pita breads.
Assemble the Greek Chicken Gyros by adding salad, sliced chicken, and a generous spoonful of tzatziki to each pita.
Wrap and serve immediately.