Preheat oven to 350 degrees. Line muffin tins with paper cups or coat with cooking spray.
Place the cream cheese, egg, 1/3 cup sugar, pumpkin puree and flour in the bowl of a stand mixer that has been fitted with the paddle attachment.
Beat until light and fluffy - the mixture may curdle at first but it will come together if you continue beating.
Stir in the chocolate chips and set aside.
In a large bowl, mix together the flour, 1 cup sugar, cocoa, baking soda and salt. Make a well in the center and add the milk, oil, vinegar and vanilla. Stir together until well blended. Fill muffin tins 2/3 full with the batter and top with 2 tablespoons of the cream cheese mixture. Sprinkle the chocolate chips over the tops of the muffins. You may end up with extra cream cheese mixture, you can put it in an oven safe dish and bake it alongside the muffins for a cheesecake snack!
Bake in preheated oven for 25 to 30 minutes, until a toothpick inserted into the center comes out clean.