Dip the rim of your martini glass into a shallow dish filled with a small amount of chocolate syrup, then into a plate filled with cocoa powder or chocolate shavings. Swirl a little chocolate syrup around the inside of the glass.
In a cocktail shaker, combine the vodka, chocolate liqueur, and Baileys. Fill the shaker with ice cubes and shake well for about 30 seconds.
Strain into the prepared martini glass, avoiding the garnished rim.
Garnish with a sprinkle of chocolate shavings or a drizzle of chocolate syrup on top and serve immediately.