Preheat the oven to 300 degrees F (150 degrees C). Grease a 9x13 inch pan.
In a medium bowl, mix together the cake mix, 1 egg and butter until well blended. The batter will be stiff. Crumble and press into the prepared pan. Sprinkle chocolate chips evenly over, and press them into the crust slightly.
For the topping, beat the cream cheese, confectioners' sugar, 3 eggs and vanilla in a medium bowl using an electric mixer until light and fluffy. Spread over the chocolate chip layer.
Bake for 45 to 50 minutes, or until golden brown. Cool completely before cutting into squares.