In a medium bowl, whisk together the Greek yogurt, oregano, olive oil, lemon juice, lemon zest, garlic, salt, black pepper, and red pepper flakes.
Place the chicken in a large food-safe bag or container. Pour the marinade over the chicken and coat well.
Cover and refrigerate for at least 30 minutes, or up to 8 hours for deeper flavor.
Preheat the oven to 375°F.
Lightly grease a baking dish with cooking spray or olive oil.
Remove the chicken from the marinade, letting the excess drip off, and arrange the pieces in a single layer in the dish.
Bake uncovered for about 45 minutes, or until the Baked Greek Yogurt Chicken is golden and the internal temperature reaches 165°F.
Sprinkle with fresh parsley before serving.
Serve warm with couscous, rice, or pita bread to soak up the flavorful juices.