Preheat the oven to 350°F. Grease and flour a 9×13 inch baking pan.
Prepare the chocolate cake mix according to package instructions and pour it into the prepared pan.
Using the end of a wooden spoon, poke holes all over the top of the warm cake.
In a medium bowl, whisk together the instant pudding mix and cold milk until thickened. Pour the pudding over the cake, making sure it fills the holes.
Spread half of the whipped topping over the pudding layer.
Melt the chocolate chips in the microwave or on a double boiler. Once melted, drizzle the chocolate over the whipped topping.
Spread the remaining whipped topping over the chocolate.
Refrigerate the cake for at least 2 hours, or until the pudding is set.
