Bring first 3 ingredients to a boil in a 2-quart saucepan. Reduce heat, and simmer 1 hour or until chestnuts are soft, adding water as necessary to keep chestnuts covered. Drain, and cool. Break chestnuts in half.
Trim brussels sprouts, and cut an "x" in stem ends.
Cook brussels sprouts in boiling salted water to cover 8 to 10 minutes or until tender; drain. Plunge into ice water to stop the cooking process; drain and set aside.
Brown pancetta in hot oil in a skillet; add chicken broth, and cook over low heat, stirring to loosen browned particles.
Arrange chestnuts and brussels sprouts in a lightly greased 12-inch gratin dish or 11- by-7-inch baking dish. Pour broth mixture over top; sprinkle with breadcrumbs, and dot with butter.
Bake at 375° for 25 minutes or until thoroughly bubbly and breadcrumbs are browned.