In a mixing bowl, whisk together olive oil, lite soy sauce, honey, minced garlic, and black pepper to make the marinade.
Add the cubed chicken to the marinade, stir to coat, and let sit for 20 minutes.
While chicken marinates, prepare the vegetables: slice the zucchini into thick rounds, and cut the bell peppers and onion into 1-inch pieces or wedges.
Thread the marinated chicken and prepared vegetables onto skewers, alternating between chicken and vegetables.
Preheat a grill or grill pan to medium-high and oil the grates to prevent sticking.
Place the kebobs on the hot grill and cook about 5 to 7 minutes per side, turning once, until the chicken is cooked through and vegetables are tender.
Remove from the grill and let rest briefly before serving.