In a large skillet over medium-high heat, melt the butter. Swirl to coat the pan and add the chicken. Toss to coat the pieces with butter and sprinkle with salt and pepper.
Cook the chicken, tossing frequently, for 3-4 minutes until cooked through. Transfer the chicken to a plate. Add oil to the pan and add the bell peppers and broccoli. Toss to coat.
Cook the vegetables, stirring constantly, for about 4 minutes. While cooking, add a splash of water (about 2 tablespoons) to the pan and scrape up any browned bits on the bottom of the pan.
When the vegetables are tender-crisp, add the chicken back to the pan along with the barbecue sauce and green onions. Stir to coat everything with the sauce and cook for about a minute to warm through. Serve warm, over rice if desired.