In a large mixing bowl, combine the cubed chicken breast with olive oil, minced garlic, dried oregano, salt, and black pepper. Toss well to ensure all chicken pieces are coated. Cover the bowl and refrigerate for at least 30 minutes, or up to 2 hours, to marinate. While chicken marinates, soak wooden skewers if using.

Thread the marinated chicken, cherry tomatoes, fresh mozzarella balls, and basil leaves onto the pre-soaked skewers in an alternating pattern. For example: tomato, chicken, mozzarella, basil, chicken, tomato, basil, mozzarella, chicken. Aim for 3-4 chicken pieces per skewer. Repeat until all ingredients are used, typically yielding 8-10 kebabs.

In a small saucepan, combine balsamic vinegar and honey (or maple syrup). Bring to a simmer over medium heat, then reduce heat to low and cook for 8-12 minutes, stirring occasionally, until the glaze thickens enough to coat the back of a spoon. It will thicken further as it cools. Remove from heat and set aside.

Preheat your air fryer to 375°F (190°C) for 5 minutes.

Arrange the kebabs in a single layer in the air fryer basket, ensuring they don't overlap (you may need to cook in batches). Air fry for 12-15 minutes, flipping them halfway through, until the chicken is cooked through (internal temperature reaches 165°F / 74°C) and slightly browned.

Carefully remove the hot kebabs from the air fryer. Drizzle generously with the prepared balsamic glaze. Serve immediately as a delicious main course.