In a large bowl, combine the barbecue sauce, olive oil, garlic powder, onion powder, smoked paprika, black pepper, and salt. Mix well to create a marinade.
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.
Preheat your grill to medium-high heat.
Thread the marinated chicken, bell pepper pieces, and onion wedges onto the skewers, alternating between chicken and vegetables.
Place the skewers on the grill and cook for 10-12 minutes, turning occasionally, until the chicken is cooked through and has nice grill marks. The internal temperature should reach 165°F.
Remove from the grill and let rest for a few minutes before serving.