Preheat oven to 350 degrees. Line a 9x5" loaf pan with parchment paper. Set aside. Over a plate, shred the zucchini. Set aside.
In a separate bowl, sift together the flour, cocoa powder, baking soda and salt. Don't skip the sifting - it's important to make sure any lumps in the cocoa powder are broken apart and well incorporated with the other dry ingredients. Begin gradually adding the dry ingredients to the wet ingredients. After all the wet and dry ingredients are combine, add in the shredded zucchini, and stir until incorporated. Fold in 2/3 cup of the chocolate chips, reserving 1/3 cup for the top of the loaf.
Pour the batter into the prepared pan. Top the batter with the reserved chocolate chips. Bake at 350 for 55-60 minutes. Test the bread by inserting a toothpick into the center of the loaf. If the toothpick comes out clean and crumb free, the bread is done.
Remove from oven, and let cool to room temperature. Remove the loaf by pulling on the excess parchment paper. Slice and enjoy right away. Store any leftovers in an airtight container at room temperature.