Preheat oven to 350 degrees F (175 degrees C). Grease a 9 inch square baking pan.
Combine cream cheese with 1/4 cup sugar and 1 egg in a mixing bowl; beat until smooth. Stir 1 cup chocolate chips into the cream cheese mixture. Set aside.
Fill a saucepan with water and bring to a boil. Turn off heat and set a heatproof mixing bowl over the water. Add butter and remaining 1 cup chocolate chips to the mixing bowl and stir until just melted. Stir in remaining 1/2 cup sugar and 2 eggs. Sift together flour, baking powder, and salt; stir into chocolate until evenly blended.
Pour half of the batter into prepared baking pan. Spread cream cheese mixture over the chocolate layer. Top with remaining chocolate mixture (this doesn't need to completely cover the cream cheese layer). Using a knife, swirl the top chocolate layer into the cream cheese to make a marble pattern, if desired.
Bake for 25 to 30 minutes or until the top is crinkled and edges pull away from sides of the pan. Cool completely, then cut into 12-16 squares. (Refrigerate before cutting to get them to look like the picture)