Coarsely chop the chocolate and melt with the rum over a hot water bath. Remove from the heat. Separate the eggs. Beat the egg yolks with half of the sugar over the hot water bath until creamy. Stir the egg yolks into the chocolate, remove from the heat and stir until cold in an ice water bath. Beat the cream until very stiff. Beat the egg whites with the remaining sugar until stiff. Fold the whipped cream into the chocolate mixture quickly before the mixture solidifies. Gently fold in the egg whites.
Pour the mousse into glasses and cover. Chill for at least 3 hours in the refrigerator. Grate the white chocolate and use to decorate the glasses. Serve cold.