Preheat oven to 350°F. Grease and flour one (1-pound) loaf pan.
In a medium bowl, whisk together the flour, cocoa powder, baking soda, baking powder, and salt.
In a large bowl, mix sugar, vegetable oil, egg, milk, and vanilla until well combined. Add the grated zucchini and mix. Using a spatula, gently add the flour mixture to the zucchini mixture and mix until incorporated and no dry flour remains. Add chocolate chips and mix.
Pour mixture onto prepared pan and bake for 50-55 minutes or until a toothpick inserted in the center of the bread comes out clean. Allow the bread to cool in the pan for 5 minutes and then carefully remove from pan; cool over a cooling rack.