In a large mixing bowl, whisk together Greek yogurt, minced garlic, lemon juice, dried oregano, olive oil, salt, and pepper. Cut the chicken breast into 1-inch chunks and add to the marinade, mixing well. Cover and refrigerate for at least 1 hour, preferably overnight.

If using wooden skewers, soak them in water for 30 minutes to prevent burning. Metal skewers can be used without soaking.

Remove marinated chicken from refrigerator and thread onto skewers, alternating with vegetables if desired, leaving space between pieces.

Preheat grill to medium-high heat. Grill kebabs for 10-12 minutes, turning occasionally, until chicken is golden brown and reaches an internal temperature of 165°F.

Remove from grill and let rest on a platter. Garnish with fresh herbs and lemon wedges, serve with tzatziki sauce.