1. Preheat the oven to 350 degrees Fahrenheit. Line two standard 12-cup muffin pans with paper or foil liners (see note).
2. To make the filling, in a medium bowl, using an electric mixer, beat the cream cheese, sugar, and egg on medium speed until smooth, about two minutes.
3. To make the cupcakes, in a medium bowl, combine the water, oil, vanilla, and balsamic vinegar. In a large bowl, whisk together the flour, cocoa, baking soda, sugar, and salt. Pour the wet ingredients into the flour mixture and stir with a wooden spoon until the batter is smooth (it will be runny).
4. Fill the muffin cups three-fourths full. Using a tablespoon measure, spoon about one tablespoon of the filling into the center of the batter. You will see the chocolate batter rise as the filling fills the middle. Fill all of the cupcakes.
5. Sprinkle the cupcakes with the chocolate chips, dividing them evenly. Put the pans in the oven and bake until a wooden skewer inserted into the center of a cupcake comes out clean, about 25 minutes. Remove the pans from the oven and set them on wire racks. Let the cupcakes cool in the pans for 10 minutes, then lift them out and set them directly on the racks. Let cool completely and serve.