Preheat your oven to 425°F (220°C).
Prepare the chicken by patting it dry and seasoning with salt and pepper.
In a large bowl, combine broccoli, bell pepper, and red onion. Drizzle with olive oil, then season with salt and pepper.
Arrange the chicken on a sheet pan and surround it with the seasoned vegetables.
Brush a generous amount of BBQ sauce over the chicken.
Roast in the preheated oven for 25-30 minutes, or until the chicken reaches an internal temperature of 165°F (74°C).
Remove from the oven and let it rest for 5 minutes before serving.