Preheat the oven to 350°F. Line two muffin pans with cupcake wrappers.
In a large bowl, whisk together the flour, cocoa powder, baking soda, baking powder and salt.
In the bowl of a stand mixer fitted with the paddle attachment, cream together the butter and sugar until light and fluffy. Add the eggs one at a time, beating between each addition. Add the sour cream and vanilla, beating until combined.
Alternately add the milk and flour mixture in three increments. Fold in the mini chocolate chips. Divide the batter among the cupcake wrappers, filling each 3/4 full.
Bake the cupcakes until a toothpick inserted comes out clean, 18 to 22 minutes. Let the cupcakes cool for 10 minutes in the pan then transfer them to a rack to cool completely.