Melt the chocolate chips in a double boiler or heavy pan over a low flame. Cool slightly. Add the one whole egg, plus two egg yolks and rum, and mix well with a mixer at low speed. Beat the remaining egg whites in a separate bowl with a mixer until stiff. Fold into the chocolate mixture.

Whip the cream until fairly stiff. Blend one cup of the cream into the pie mixture. Reserve the remaining cup for the pie top. Carefully spoon the filling into the pie shell and refrigerate. To serve, spread the remaining cup of whipped cream over the pie. If desired, garnish with a few chocolate shavings.