Melt butter in a frying pan over medium heat; add sugar and stir until well blended. Stir in rum bring to a boil and simmer for 3-5 minutes. Add chestnuts and stir until coated with the caramel mixture.
Line a cookie sheet with parchment paper, place individual chestnuts on paper and cool for about 1 hour, until coating has hardened.
Serve as a delicious Holiday snack, or a unique addition to your favorite salad!