Preheat the oven to 350 degrees Fahrenheit. Line a 9x13 pan with parchment paper.
Add the sugar, oil, and vanilla extract to a large bowl, and stir them together well with a hand mixer, or stand mixer.
Add the flour, cocoa powder, baking soda, and salt. Mix them together until the mixture is dry and crumbly.
Add in the shredded zucchini, and fold it into the batter until it is combined evenly. (The batter will be very thick still) Let the batter sit for 5 to 10 minutes to help the zucchini release some moisture. (The batter with still be thick, but spreadable).
Fold the chocolate chips into the batter.
Spread the batter into the prepared pan, making sure to push it all the way to the edges, and corners.
Bake the brownies for 25-30 minutes, or until the tops of the brownies spring back when touched lightly with a finger.
Let the brownies cool for about 30 minutes.