1. Preheat oven to 400 degrees.
2. Pour olive oil in a 13" x 9" baking dish. Lightly dredge the chicken through to coat it, then place chicken breasts side by side in the dish.
3. In a small bowl, whisk together salt, pepper, garlic powder, onion powder and chili powder. Sprinkle the seasoning mixture over both sides of the chicken and rub it in with your hands. Place chicken breasts side by side, making sure there is no overlap. Toss broccoli in olive oil and sprinkle lightly with salt. Place next to the chicken.
4. Bake in a preheated oven for 15-20 minutes, until juices are clear or a meat thermometer reads 160-170 degrees.