Preheat your oven to 375°F (190°C) and prepare a madeleine pan.
In a bowl, whisk together the flour, cocoa powder, baking powder, and salt.
Melt the butter and let it cool slightly before mixing it with the powdered sugar.
Add eggs one at a time to the butter and sugar mixture, mixing well after each addition.
Stir in the vanilla extract until combined.
Gradually fold in the dry ingredients until just combined; be careful not to overmix.
Gently fold in the chocolate chips, reserving some for placing on top.
Spoon the batter into the madeleine molds, filling them about 3/4 full.
Top each madeleine with a few reserved chocolate chips.
Bake for 10-12 minutes or until the edges are firm but the centers are soft.
Allow the madeleines to cool for a few minutes in the pan before transferring to a rack.