Preheat the oven to 350F and butter an 9x5 loaf pan.
Wrap the shredded zucchini in cheesecloth and squeeze as much liquid out as you can. Set aside.
Whisk together the flour, cocoa, salt, baking soda, and baking powder. Set aside.
Whisk together the eggs, milk, melted butter, brown sugar, and vanilla extract. Add the zucchini and dry ingredients, then fold in the chocolate chips.
Pour the batter into the prepared pan and bake for 55-60 minutes, or until a cake tester comes out clean.
Let the loaf cool for 15 minutes in the pan before removing it. Serve warm or cooled!
Notes
Depending on your flour, you may need more or less liquid. The batter should be quite thick, but still wet.
Recipe by The Kitchen Paper at http://c02.ddd.mwp.accessdomain.com/whole-wheat-chocolate-zucchini-bread/