To make a marinade, process all the ingredients for kabobs (except chicken) in a food processor for 30 seconds, until blended. Transfer the mixture to a ziplock bag and add the cubed chicken. Put in a fridge and marinate for at least 2 hours.
Prepare the veggies. In a bowl, add the bell peppers, zucchini slices, and red onions. Drizzle with olive oil, add salt and pepper to taste.
Remove the chicken from a fridge and from the marinade. Thread it onto skewers together with the veggies. If using wooden skewers, soak them in water for 30 minutes beforehand.
Preheat oven to 425°F (220°C) or prepare a fire in a charcoal grill, or preheat a broiler.
If using a grill or a broiler: Place the skewers on an oiled grill rack or a broiler pan and cook, turning once, for about 5 minutes per side, or until no longer pink.
If cooking in oven: Line a baking sheet with foil. Place a cooling rack on top. Place the skewers on a cooling rack and bake, turning once, for 20-25 minutes, or until no longer pink.