Preheat the oven to 350 Degrees F. Butter and dust a loaf pan with cocoa powder.
In a large bowl whisk together the flour, cocoa powder, baking soda, cinnamon, and salt.
In another large bowl mix together the sugar and egg and egg yolk until smooth. Add melted butter and vanilla extract and mix until smooth. Add the grated zucchini, then add the flour mixture in 3 additions. Fold in the chocolate chips.
Pour the batter into the prepared baking dish and bake for 50 minutes. Let cool slightly in pan, then transfer to a cooling rack.