In a bowl, whisk together soy sauce, brown sugar, ginger, garlic, sesame oil, and rice vinegar until sugar is dissolved.
Reserve 1/4 cup of the marinade for basting later.
Place the chicken cubes in a large bowl or resealable bag and pour the remaining marinade over them. Refrigerate for 30 minutes.
If using wooden skewers, soak them in water for at least 20 minutes to prevent burning.
Preheat grill to medium-high heat (400°F/200°C) and lightly oil the grates.
Thread the marinated chicken, pineapple, bell peppers, and red onion alternately onto the skewers.
Place skewers on the grill and cook for 12 to 15 minutes, turning every 3 to 4 minutes to ensure even cooking.
During the final 5 minutes of grilling, brush the reserved marinade onto the chicken and fruit.
Remove from grill once chicken reaches an internal temperature of 165°F (74°C).
Allow to rest for 3 minutes before serving.