In a medium bowl, slowly melt the chocolate over a double boiler or on half power in a microwave. Once completely melted, whisk in the cocoa powder and sugar.
In a saucepan, heat the milk. Keeping the milk hot, pour about 1/4 cup of it over the chocolate and mix vigorously. Repeat with another 1/4 cup milk. Drizzle in the remainder while whisking constantly.
Pour about one tablespoon of chartreuse in the bottom of each of four small mugs. Top with hot chocolate and a dollop of softly whipped cream. Serve immediately.