Preheat oven to 350 degrees . Butter and dust a 9 x 5-inch loaf pan with cocoa powder.
In a medium bowl, whisk together flour, cocoa powder, baking soda, cinnamon, and salt; set aside.
In a large bowl, cream together sugar and butter until smooth and creamy. Add egg, egg yolk and vanilla extract, beat until well combined. Stir in zucchini. Add flour mixture in 3 additions, beating after each addition. Fold in chocolate chips.
Pour batter into the prepared loaf pan and bake for 50-55 minutes or until a tooth pick inserted into the middle comes out clean. Cool in the pan for 5-10 minutes; remove to a wire rack to cool completely.