Combine the chicken marinade ingredients in a zip-top bag or dish: olive oil, soy sauce, lemon juice, brown sugar, Worcestershire sauce, garlic, Italian seasoning and black pepper. Squish to mix in the bag or whisk if using a dish.
Add the chicken pieces to the marinade. Make sure that all of the chicken is coated with the marinade. Refrigerate for at least 30 minutes and up to 4 hours.
If using wooden skewers, soak them in a dish of warm water for at least 20 minutes.
Place the zucchini rounds and chopped bell peppers in a baking dish or bowl. Drizzle with the 1 ½ tablespoons of olive oil and sprinkle with salt and pepper; toss gently to coat. Add the onion to the bowl last and mix in very gently so that the onion layers stay together as best as possible.
Put the chicken and vegetables on the skewers, dividing evenly between the 8 skewers and arranging the vegetable pieces in between the chicken pieces.
Grill over medium heat for 12-18 minutes, turning every few minutes to cook all sides evenly. Kabobs are done when chicken is cooked through to an internal temperature of 165° F.
NOTE: Can also bake at 425 for approximately 25 minutes.
