Preheat oven to 350 degrees F. Grease and flour an 8x4-inch loaf pan; set aside.
In a medium bowl, whisk together the flour, cocoa powder, salt, baking powder and baking soda; set aside.
In a large bowl, whisk together the eggs, vegetable oil, brown sugar, honey and vanilla extract. Add the flour mixture to the wet ingredients and use a rubber spatula to gently fold the batter together until almost no flour remains. Stir in the zucchini and chocolate chips, ensuring they are evenly distributed.
Pour the batter into the prepared loaf pan and bake for 65 to 75 minutes, or until a toothpick (or thin knife) inserted into the center comes out with just a few moist crumbs attached. Allow to cool in the pan for 15 minutes, then turn out onto a cooling rack to cool completely before slicing. Store leftovers at room temperature, tightly wrapped in plastic wrap.