Special equipment: cocktail shaker
Combine the chocolate and 1/4 cup water in a small bowl and place over a pan of barely simmering water. Stir until the chocolate is completely melted and the mixture is smooth, 2 minutes. Set aside to cool slightly.
Dip the rims of 4 martini glasses into the melted chocolate, allowing any excess chocolate to drip back into the bowl. Chill the glasses in the freezer for 10 minutes.
In a pitcher, mix together the espresso, coffee liqueur and vodka. Fill a cocktail shaker with ice. In batches, add the vodka mixture and shake for 10 seconds. Strain the mixture into the prepared glasses and serve.