In a medium bowl, whisk together soy sauce, brown sugar, rice vinegar, sesame oil, garlic, ginger, and black pepper.
Add the chicken cubes to the marinade, ensuring they are well coated. Cover and refrigerate for at least 30 minutes, or up to 2 hours for more flavor.
If using wooden skewers, soak them in water for at least 30 minutes to prevent burning.
Preheat your grill or grill pan over medium-high heat.
Thread the marinated chicken, bell pepper, and onion onto the skewers, alternating the ingredients.
In a small bowl, mix cornstarch and water to create a slurry. Brush this mixture onto the skewers for a glossy finish.
Grill the skewers for about 10-12 minutes, turning occasionally, until the chicken is cooked through and reaches an internal temperature of 165°F.
Remove from the grill and let rest for a few minutes before serving.