In a medium saucepan, heat the cream until bubbles appear around the edge. Remove the pan from the heat, add the chocolate and let stand for 1 minute, then stir until smooth.
Whisk the egg yolks in a small bowl, then whisk in 1/2 cup of the hot chocolate cream. Scrape this mixture into the saucepan and whisk constantly until smooth. Stir in the rum and butter. Pour the custard into eight 1/2-cup ramekins or espresso cups and refrigerate until chilled, at least 4 hours.