Step 1Heat the oven to 550 degrees. With a small knife, score the chestnuts with an "X" on the flat side of the shell. Roast them on a baking sheet until the shells where they have been scored curl and darken, 12 to 15 minutes. Remove the chestnuts from the oven and immediately cover them with a towel that has been soaked in ice water and wrung out. When the chestnuts are cool enough to handle, peel away the shells and the thin skin covering the chestnut.
Step 2With a small pointed knife, remove the peel in a spiral from the orange.
Step 3In a medium frying pan, melt the butter. Add the sugar, the orange peel and orange liqueur.
Step 4Stir the syrup and let it thicken but not caramelize. Add the chestnuts and stir them gently into the syrup. Add the juice of half the orange and, when the chestnuts are warmed through, pour in the rum and flambe it by lighting it with a long match.
Step 5After the flame has died out, spoon the chestnuts with the syrup over vanilla ice cream.