With a small knife, cut an "X" into the root ends of the onions and Brussels sprouts. In a large pot of boiling water, blanch onions for 3–4 minutes. Remove with a slotted spoon and place in a medium bowl. Put the Brussels sprouts in the water. Blanch for 3–4 minutes. Pour into a colander and rinse with cold water. Set aside.
In a 3–quart saucepan over medium-high heat, warm the maple syrup for 4 minutes. Add the vinegar and the onions. Reduce the heat to medium and simmer for 20–30 minutes, or until the liquid has almost evaporated.
(The recipe may be prepared up to this point one day ahead. Cover and refrigerate. Rewarm the onions before proceeding.)
Add the chestnuts and brussels sprouts. Stir gently to combine. Cook for about 5 minutes, or until the Brussels sprouts are thoroughly heated but still green. Season with the pepper, and serve warm or at room temperature. Serves 12.
*To prepare chestnuts: place in boiling water for 15–25 minutes, then drain. Shells and skins are easier to remove after boiling.