Preheat the oven to 350F and line a 12-count muffin pan with paper liners. For easy release, lightly spray each cupcake liner or use foil liners.
Shred the zucchini with a cheese grater or in a food processor and ring out the excess moisture with a paper towel or clean kitchen cloth. Set aside.
In a medium bowl, combine the flour, cocoa powder, baking powder, and baking soda.
In a separate large bowl, mash the banana with a fork. Add the eggs and vanilla extract, and whisk to combine.
Slowly add the dry ingredients into the wet ingredients, and stir until you achieve a smooth chocolate batter. Add in the shredded zucchini and chocolate chips, folding to combine.
Fill each muffin cup ¾th full, and bake for 25 minutes or until a toothpick inserted in the center comes out clean.
Remove the pan from the oven and allow the muffins to cool down for 5 minutes before serving.