If fresh chestnuts are used, preheat the oven to 375°F and score the chestnuts at the base with a paring knife.
Toast the chestnuts on a baking sheet in the oven for about ten minutes until the meat shrinks from the shell.
Shell and skin the chestnuts while they are warm, as the shells can be easily removed.
If canned chestnuts are used, drain and dry them.
Bring a large pot of salted water to a boil.
Trim the outside leaves from the brussels sprouts and cut a cross 1/4 inch deep in the bottom of each.
Drop them in the boiling salted water and cook until they are fork-tender, about 5 to 7 minutes.
Drain the sprouts and drop them into ice water to stop the cooking.
Cut each sprout in half.
Heat the maple syrup in a medium saute pan over medium heat.
Add the brussels sprouts and bring to a boil.
Quickly add the chestnuts and stir in the butter.
The syrup and butter will thicken and glaze the sprouts.
Season to taste with salt and pepper.