Preheat oven to 350 and set aside a 13 x 9 pan, ungreased.
For the crust, place the cake mix, melted butter and egg in a mixing bowl. Blend on low for 2 minutes. The batter should come together in a ball. Pat the batter evenly over the bottom of the 13 x 9 pan. Set aside.
For the filling, place the cream cheese in the same mixing bowl and blend on low until fluffy. Add the eggs, vanilla and melted butter and beat on medium for 1 minute. Add the confectioners sugar and beat until this is well incorporated. Place the chocolate chips in a small saucepan over low heat (or you can microwave them, too) and cook, stirring until the chips are melted. Measure out 1 cup of the cream cheese filling and fold it into the chocolate mixture, stirring so the batter becomes well blended and all one color. Set aside.
Pour the remaining filling onto the crust and spread with spatula so that the filling covers the entire surface. Drop spoonfuls of the chocolate batter over the top of the filling, then swirl them with a dinner knife so the top of the batter has a marbled effect. Be careful not to cut through the crust.
Bake 45-47 minutes. Remove the pan and place it on a wire rack to cool, 30 minutes. Cut into squares and serve.