In a small bowl, whisk together the Greek yogurt, grated cucumber, lemon juice, and minced garlic to create the tzatziki sauce; set aside in the refrigerator.
Season the chicken breast evenly with dried oregano, garlic powder, sea salt, and black pepper.
Heat the olive oil in a medium skillet over medium-high heat.
Add the chicken to the skillet and cook for 5-7 minutes per side, or until the internal temperature reaches 165°F and the exterior is golden brown.
Remove the chicken from the pan, let it rest for 3 minutes, then slice it into thin strips.
Lightly warm the whole wheat pita in the same skillet or a toaster oven until soft and pliable.
Assemble the gyro by spreading a generous layer of tzatziki on the pita, followed by the sliced chicken, tomato, cucumber slices, and red onion.
Fold the pita and serve immediately while warm.