Cut the chicken breast into 1-inch cubes and set aside in a medium mixing bowl.
In a small bowl, whisk together the Greek yogurt, olive oil, lemon juice, dried oregano, garlic powder, sea salt, and black pepper to create the marinade.
Pour the yogurt mixture over the chicken cubes, tossing well to ensure every piece is evenly coated.
Cover the bowl and refrigerate for at least 30 minutes to allow the enzymes in the yogurt to tenderize the meat.
While the chicken marinates, chop the red bell pepper and red onion into 1-inch pieces suitable for skewering.
Thread the marinated chicken, bell peppers, and onions onto wooden or metal skewers, alternating between the meat and vegetables.
Preheat a grill or grill pan to medium-high heat and lightly grease with a mist of oil.
Grill the skewers for 10-12 minutes, turning every few minutes, until the chicken is golden brown and reaches an internal temperature of 165°F.
Serve the skewers over a bed of warm quinoa and garnish with a sprinkle of crumbled feta cheese.