Bring 2 quarts of water and 1 teaspoon of salt to a boil.
If fresh chestnuts are used, shell with a paring knife and toast on a cookie sheet in the oven until the meat pulls from the shell and the shell and skin can be easily removed. If canned chestnuts are used, drain and dry them.
Trim the outside leaves from the Brussels sprouts and cut 1/4-inch deep cross in the bottoms of each. Drop them in the boiling salted water and cook until they are fork tender. Drain the sprouts and drop into ice water to shock and cool. Cut each Brussels sprout in half.
Add the maple syrup to a 10-inch saute pan and warm. Add the Brussels sprouts and bring to a boil. Quickly add the chestnuts and stir. The syrup will thicken and glaze the sprouts.