In a bowl, whisk together Greek yogurt, olive oil, lemon juice, garlic, oregano, paprika, salt, pepper, parsley, and onion powder until smooth.
Add chicken and mix until fully coated in the greek yogurt chicken marinade.
Cover and refrigerate for at least 2 hours or overnight for best flavor.
Cut vegetables into even-sized chunks.
Thread chicken, peppers, and onion onto skewers, alternating pieces.
Preheat grill to medium-high heat and lightly oil grates.
Grill kabobs for 10–12 minutes, turning occasionally, until chicken is fully cooked (165°F / 74°C).
Remove from grill and let rest for 5 minutes.
Garnish with parsley, lemon juice, and feta if desired.
Serve warm.