Wash and trim the sprouts. Soak them in four cups cold water containing one teaspoon salt for twenty minutes. Drain.
Place in a saucepan with the onion, stock and remaining salt. Bring to a boil and cook, uncovered, for five minutes. Cover and cook for ten to twelve minutes longer, or until sprouts are tender. Drain.
Melt the butter, add the chestnuts, and cook until butter is golden. Pour over sprouts and toss lightly to mix sprouts and chestnuts.