Cut the chicken breasts into 1-inch pieces and place in a large Ziploc bag, bowl, or shallow baking dish. Set aside.
In a medium bowl, combine the Greek Yogurt, garlic, olive oil, lemon zest, fresh lemon juice, red wine vinegar, oregano, paprika, salt, and pepper. Whisk until smooth.
Pour the marinade over the chicken and stir to coat. If you are using a bag, add the marinade to the bag and seal it tight, removing as much air as possible. Move the chicken around, making sure it is well coated.
Place in the refrigerator and let marinate for 30 minutes or up to 4 hours.
If you are using wooden skewers, make sure you soak them in water for 20 minutes before adding the chicken.
Remove the chicken from the marinade and thread on skewers, about 4 ounces of chicken per skewer. Discard remaining marinade.
Preheat the grill to a medium-high heat. You can also use a grill pan. Brush the grill or grill pan with olive oil to make sure the kabobs don’t stick.
Grill the chicken until fully cooked through, about 10 minutes, turning the skewers every couple of minutes.
Remove from the grill and place on a serving platter. Garnish with feta cheese and fresh parsley. Serve warm with tzatziki sauce. You can also serve hummus, pita bread, and a simple Greek salad on the side.