Preheat oven to 350°F (177°C).
Grease a 9x13-inch baking pan.
Finely shred zucchini and lightly blot excess moisture with paper towels.
In a medium bowl, whisk together flour, cocoa powder, baking soda, baking powder, and salt.
In a large bowl, whisk together vegetable oil, applesauce, brown sugar, granulated sugar, eggs, and vanilla extract until smooth.
Stir shredded zucchini into the wet mixture.
Gradually add dry ingredients into wet ingredients and mix until just combined.
Fold in chocolate chips.
Pour batter evenly into prepared baking pan.
Bake for 32–38 minutes or until a toothpick inserted in the center comes out mostly clean.
Allow cake to cool completely before frosting or serving.