In a spacious mixing bowl, whisk together the olive oil, lemon juice, lemon zest, minced garlic, dried oregano, dried thyme, and a generous pinch of salt and pepper. Add the chicken thighs to the bowl and toss until they're thoroughly coated with the marinade. Cover the bowl with plastic wrap and refrigerate for at least 1 hour (or up to overnight for a more intense flavor infusion).
Preheat your grill or grill pan to a medium-high temperature. Once hot, remove the chicken from the marinade, discarding any leftover liquid. Grill the chicken for approximately 6-7 minutes on each side or until it is thoroughly cooked and reaches an internal temperature of 165°F (75°C). After grilling, allow the chicken to rest for a few minutes before slicing into strips.
While the chicken can be cooking, prepare a refreshing tzatziki sauce. In a small mixing bowl, combine the Greek yogurt with the diced cucumber, a splash of lemon juice, and a sprinkle of salt and pepper. Mix well until combined and set aside to let the flavors meld.
Warm the pita breads on the grill for about 1 minute on each side until they are soft and pliable. Once warmed, place several slices of grilled chicken in the center of each pita. Top with a generous dollop of the tzatziki sauce, followed by diced tomatoes and the thinly sliced red onions.
Finish off each gyro with a sprinkle of chopped fresh parsley for a burst of color and flavor. Serve immediately, with additional tzatziki sauce on the side for dipping if desired.