In a medium bowl, whisk together the olive oil, lemon juice, fresh parsley, minced garlic, salt, and black pepper to create the marinade.
Place the chicken pieces in a large resealable plastic bag or shallow dish. Pour the marinade over the chicken, seal or cover, and toss to coat evenly. Refrigerate for at least 30 minutes, or up to 4 hours.
If using wooden skewers, submerge them in water to soak for 30 minutes prior to grilling to prevent burning.
Preheat the grill to medium-high heat, approximately 400°F.
Thread the marinated chicken pieces onto the skewers, alternating with the zucchini, red bell pepper, yellow bell pepper, and red onion pieces.
Place the assembled skewers on the hot grill. Cook for 10 to 12 minutes, turning every 3 to 4 minutes, until the chicken reaches an internal temperature of 165°F and the vegetables are tender with a light char.
Remove the kabobs from the grill and let them rest for 3 to 5 minutes before serving.