Preheat the oven to 350F. Line a 9x9 baking dish with parchment paper so that the paper hangs over opposite sides. Set aside.
Shred the zucchini in a food processor with the shredder attachment or with a handheld shredder. Set aside.
In a stand-up mixer or large mixing bowl, mix together the oil, sugar, and vanilla extract. In a separate bowl combine the flour, cocoa powder, baking soda, and salt. With the mixer running, slowly add the dry ingredients to the wet, beating it until it's well combined. The dough will be dry at this point. Don't worry. The zucchini provides the moisture.
Add the zucchini and gently mix together. Fold in the chocolate chips.
Pour the batter onto the prepared baking sheet and bake for 35-45 minutes. You want the brownies to be slightly under-baked so that a knife inserted in the middle comes out with moist crumbs on it.
Let the brownies cool completely before taking them out of the baking dish. When ready to remove from the pan, pull up on the overhanging parchment paper. Slice into 2" pieces.