Preheat the oven to 170°C (150°C fan forced). Grease and flour a 2.5-litre (24cm) fluted tube (bundt) cake pan. Remove the enclosed frosting sachet from the cake mix and reserve for another use.
Make up the cake mix as directed on the box using the oil, eggs and water, then fold through the chocolate chips. Pour the mixture into the cake pan in an even layer.
Make the filling. In a small bowl, beat the cream cheese until smooth, then whisk in the caster sugar, flour and egg. Spoon over the cake mixture. Gently run a knife through the mixture in a zigzag pattern. Do not mix too thoroughly.
Bake in the oven for 45-55 minutes or until a skewer inserted into the centre of the cake comes out clean. Cool in the pan for 10 minutes, then turn the cake out onto a wire rack to cool completely; about 1 hour.
Make the topping. In a small bowl, beat the cream cheese until smooth. Add in the icing sugar and mix until smooth. Spoon over the cake and let it run partially down the sides.
Spoon the chocolate frosting into a disposable piping bag and cut a small hole in the end. Pipe the frosting over the top of the cake and serve in slices.