In a bowl, combine the olive oil, lemon juice, minced garlic, dried oregano, dried thyme, paprika, salt, and black pepper. Mix well to create the marinade.
Add the chicken breast cubes to the marinade and toss until they are evenly coated. Let the chicken marinate for at least 30 minutes, or refrigerate for up to 4 hours for more flavor.
Preheat your air fryer to 400 degrees F / 200 degrees C for about 5 minutes.
Thread the marinated chicken pieces onto the soaked wooden skewers, leaving a little space between each piece.
Place the chicken skewers in a single layer in the air fryer basket, without overcrowding.
Cook the chicken souvlaki in the air fryer for 10-12 minutes, flipping halfway through the cooking time, until the chicken is cooked through and has a golden brown exterior.
Once cooked, remove the chicken souvlaki from the air fryer and let it rest for a few minutes before serving.
Serve with pita bread, tzatziki sauce, sliced tomatoes, onions, and any other desired accompaniments.