Prepare the Marinade: In a large bowl, combine the lime juice, red wine or cider vinegar, olive oil, oregano, salt, and grated garlic. Mix ingredients together until well combined.
Marinate the Chicken: Add the chicken pieces to the marinade, ensuring they are well coated. You can cook the chicken immediately or let it marinate in the refrigerator for 30 minutes to 1 hour. The longer you marinate, the zestier the chicken will become. You can marinate the chicken up to 24 hours in advance.
Preheat the Air Fryer: If your air fryer requires preheating, set it to 390°F and allow it to preheat for a few minutes.
Thread the Chicken: Thread the marinated chicken pieces onto skewers. If you are using wooden skewers, be sure to soak them in water for at least 30 minutes before threading the chicken to prevent them from burning.
Cook the Chicken: Place the skewers in the air fryer basket in a single layer. Cook at 390°F for 15 or so, turning the skewers halfway through the cooking time. The chicken should be golden brown and cooked through, with an internal temperature of 165°F (75°C).
Serve: Pair the chicken souvlaki with your favorite sides such as rice, salad, grilled vegetables, or mashed potatoes.