Preheat the oven to 350 degrees. Line two 12-cup muffin pans with paper or foil baking cups.
Using an electric mixer, combine the cream cheese, 1 cup sugar and ⅛ teaspoon salt. Add the egg and mix well. Fold in the chocolate chips and set aside.
In a large mixing bowl, whisk together the flour, the remaining 1½ cups sugar, ¾ teaspoon salt, the baking soda and cocoa powder.
Add water, oil, vinegar and vanilla and stir until smooth.
Fill each baking cup two-thirds full with the cake batter and top with 1 tablespoon of the cream cheese mixture.
Bake until the edges are firm to the touch, about 23 minutes.