Preheat the oven to 350°F (325°F for dark or nonstick pans) and line 24 regular-size muffin cups with paper baking cups.
In a medium bowl, use an electric mixer on medium speed to blend cream cheese, sugar, and 1 egg until smooth. Then, fold in 1 cup of chocolate chips and set aside.
Combine cake mix, water, oil, and eggs in a large bowl. Mix on low speed for 30 seconds, then increase to medium speed and beat for 2 minutes. Fill muffin cups with 1/4 cup of batter each. Add a heaping teaspoon of cream cheese mixture on top of each.
Bake for 21 to 27 minutes or until tops spring back when lightly touched, then cool in pans for 10 minutes. Remove from pans and transfer to cooling racks. Allow to cool completely, about 30 minutes.
Cover the cake with a generous layer of frosting and sprinkle with the remaining 1/2 cup of chocolate chips. Store it loosely covered in the refrigerator.