Preheat your oven to 350°F (175°C). Grease a 9x13-inch baking dish.
In a large mixing bowl, combine the chocolate cake mix, water, vegetable oil, and eggs. Mix until well combined and smooth.
Pour the cake batter into the prepared baking dish and spread it evenly.
In another bowl, beat the softened cream cheese until smooth. Gradually add the powdered sugar and cocoa powder, mixing until fully combined.
Stir in the milk and vanilla extract until the mixture is smooth and creamy.
Drop spoonfuls of the cream cheese mixture over the cake batter. Use a knife or spatula to swirl the cream cheese mixture into the cake batter gently.
Sprinkle the chocolate chips evenly over the top.
Bake in the preheated oven for 30-35 minutes, or until the edges are set but the center is still slightly gooey.
Allow the cake to cool for about 10 minutes before serving. It can be served warm or at room temperature.