Preheat the oven to 400 degrees. In a large bowl, toss together the potatoes, onions, 1 tablespoon of the olive oil, salt, pepper, garlic powder, paprika, and chili powder. Spread in an even layer on a baking sheet and roast for 20-30 minutes, or until fork-tender.
Remove the potatoes from the oven and toss the broccoli with 1 tablespoon of the olive oil. Move the potatoes to only take up 1/2 of the baking sheet and spread the broccoli on to the second half of the baking sheet next to the potatoes. Return to the oven and roast for another 10 minutes.
Heat one tablespoon of the olive oil in a large skillet on high heat. Once hot, add the chicken and cook until firm and no pink remains. Drain off any excess liquid. Stir in the BBQ sauce and bring to a simmer. Remove from heat.
Remove the potatoes from the oven and spoon the potatoes into 1/3 of a serving bowl. Spoon the broccoli into a second 1/3, and finally, fill the remaining space with the chicken. Serve and enjoy!