Preheat the oven to 350°F (175°C) and grease a 9x9 inch baking pan.
In a large mixing bowl, whisk together the vegetable oil, granulated sugar, and vanilla extract until well combined.
In a separate medium bowl, sift together the all-purpose flour, unsweetened cocoa powder, baking soda, and salt.
Stir the dry ingredients into the oil and sugar mixture; the resulting dough will be dry and crumbly.
Fold in the shredded zucchini by hand and allow the mixture to rest for 5 minutes until the zucchini releases enough moisture to form a thick batter.
Fold in the chocolate chips and spread the batter evenly into the prepared baking pan.
Bake for 25 to 30 minutes or until the top springs back when lightly touched and a toothpick inserted in the center comes out clean.
Allow the brownies to cool completely in the pan on a wire rack before slicing into squares.