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 1/8 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 1-1/2 cups sugar, 3/4 teaspoon salt, the baking soda and cocoa powder. Add 1-1/2 cups water, the 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 25 minutes.