Heat oven to 350 degrees. Lightly grease and flour the bottom only of a 9 x 13 inch glass baking dish.
In a large mixing bowl combine the cake mix, pudding mix, water, vegetable oil, vanilla, and eggs.
Mix on low for about 30 seconds, and then on medium speed for about 2 minutes.
Pour cake batter into prepared pan.
In another large mixing bowl, beat the cream cheese, sugar, and egg with hand mixer on medium speed until smooth and creamy.
Fold in the chocolate chips.
Spoon the cream cheese filling by tablespoonfuls over the batter.
Using a table knife, swirl the cream cheese batter back and forth, then turn the pan and swirl it in the opposite direction. When swirling the cream cheese batter, be sure it goes down into the cake batter, not just on the surface.
Bake for 35-40 minutes or until a toothpick inserted comes out clean.
Cool completely before frosting.
In a medium sized bowl, beat together the butter, cocoa, milk, vanilla, and powdered sugar until until creamy and well blended.
Frost the cooled cake.