Preheat your grill or grill pan over medium-high heat.
In a bowl, mix olive oil, oregano, garlic powder, salt, and pepper. Rub this mixture all over the chicken breasts.
Grill the chicken for 6-7 minutes on each side or until cooked through and juices run clear. Remove from the grill and let it rest for a few minutes.
While the chicken is resting, prepare a quick tzatziki sauce by combining Greek yogurt, lemon juice, and a pinch of salt in a small bowl.
Slice the grilled chicken into thin strips.
Carefully warm the pita breads in a skillet or microwave for about 10 seconds until soft and pliable.
To assemble, open each pita pocket and fill with slices of grilled chicken, followed by cherry tomatoes, cucumber, red onion, and a generous sprinkle of feta cheese.
Drizzle the tzatziki sauce over the stuffed pitas and garnish with fresh parsley.
Serve immediately with extra lemon wedges on the side for drizzling.