In a medium bowl, whisk together the ketchup, brown sugar, soy sauce, pineapple juice, 2 tablespoons olive oil, rice vinegar, garlic, ginger, sesame oil, black pepper, and salt if desired.
Reserve ½ cup of the marinade for basting and refrigerate it.
Place the chicken cubes in a large resealable bag and pour the remaining marinade over the chicken. Seal the bag and refrigerate for 1 hour. Do not marinate longer to prevent the pineapple juice from affecting the chicken's texture.
While the chicken marinates, soak the wooden skewers in water for at least 1 hour.
Preheat the grill to medium heat, about 400°F (200°C).
Toss the pineapple, bell peppers, and red onion with the remaining 2 tablespoons olive oil. Season the onions and peppers lightly with salt and pepper.
Thread the chicken, pineapple, peppers, and onion alternately onto the skewers.
Lightly oil the grill grates and place the Hawaiian Chicken Kebabs on the grill.
Grill for 5 minutes, then brush the tops with half of the reserved marinade.
Flip the skewers, brush with the remaining marinade, and continue grilling for another 4–5 minutes, or until the chicken reaches an internal temperature of 165°F (75°C).
Remove from the grill and serve immediately while warm.