Preheat your oven to 400°F (200°C).
In a large mixing bowl, combine the BBQ sauce, garlic powder, onion powder, salt, and pepper. Add the chicken breasts and coat them well with the marinade. Allow to marinate for at least 10 minutes while you prepare the vegetables.
In the same bowl or another, toss the broccoli, bell peppers, and red onion with olive oil, salt, and pepper until evenly coated.
Line the baking sheet with aluminum foil for easy clean-up (optional). Lay the marinated chicken breasts in the center of the sheet pan.
Arrange the vegetables around the chicken in a single layer.
Bake in the preheated oven for about 25-30 minutes, or until the chicken is cooked through (internal temperature of 165°F/75°C) and the vegetables are tender.
If desired, brush additional BBQ sauce over the chicken during the last 5 minutes of cooking for extra flavor.
Remove the pan from the oven. Let the chicken rest for a few minutes before slicing.
Serve the chicken with the roasted vegetables on the side.