1. Preheat oven to 400°.
2. Combine sprouts and chestnuts in a large bowl. Add oil, salt, and peppers; toss well to coat. Spread in a single layer on a jelly-roll pan.
3. Bake at 400° for 25 minutes or until sprouts are tender, stirring after 15 minutes. Remove from oven. Add butter to sprout mixture, tossing until butter melts.