
Marinate the chicken. Using a sharp knife, cut the chicken into 1-inch cubes and cut the onion and bell peppers into 1-inch pieces. In a large bowl or gallon-size zip-top bag, combine the olive oil, white wine vinegar, Parmesan cheese, garlic, sugar, Italian seasoning, black pepper, and Kosher salt. Add the chicken and veggies to the marinade, then toss until everything is coated. Cover the bowl (or seal the bag), then place in the refrigerator for at least 2 hours, or overnight.
Preheat the grill. Set your grill to medium-high heat (about 400-450 degrees F). While the grill is heating up, clean and oil the grates to prevent sticking. If using wooden skewers, soak them in water for at least 30 minutes before threading the kabobs.
Thread the kabobs. Remove the chicken from the marinade, shaking off any excess, then thread it onto skewers. Alternate the chicken with the other ingredients for variety and color.
Grill the kabobs. Place the kabobs on the grill and cook for 12-15 minutes, turning every 3-4 minutes to ensure even cooking on all sides.The chicken is done when it reaches an internal temperature of 175 degrees F (165 degrees F for breasts) with a reliable meat thermometer and the juices run clear.
Rest and serve. Remove the kabobs from the grill to a serving platter, then let them rest for 3-5 minutes before serving hot with breads, dips, or your other favor kabobs.