Preheat your oven to 350°F (175°C).
Place the pie crust in a 9-inch pie pan and blind bake it for about 10 minutes, until lightly golden. Remove from the oven and let cool.
In a saucepan over low heat, melt the semi-sweet chocolate chips, stirring frequently until smooth. Remove from heat and allow it to cool slightly.
In a mixing bowl, whisk together the eggs and granulated sugar until well combined and slightly frothy.
Add the melted chocolate, heavy cream, dark rum, vanilla extract, and salt to the egg mixture. Stir until everything is incorporated and smooth.
Pour the chocolate filling into the cooled pie crust.
Bake the pie in the preheated oven for 25-30 minutes, or until the filling is set but slightly jiggly in the center.
Remove the pie from the oven and allow it to cool at room temperature for 15 minutes. Then refrigerate for at least 2 hours or until chilled and firm.
Serve cold or at room temperature, garnished with whipped cream and chocolate shavings if desired.