Preheat the oven to 350 degrees F (175 degrees C). Spray a 9-inch square pan with cooking spray.

Combine sugar, brown sugar, and olive oil in a large bowl; beat with an electric mixer until well combined. Mix in vanilla extract. Add flour, cocoa powder, baking soda, and salt and mix until combined. (Mixture will be dry).

Add zucchini and mix with a spoon until incorporated. Allow to sit for 5 minutes until mixture becomes more wet. Stir in vegan chocolate chips. Transfer batter to the prepared pan.

Bake in the preheated oven until top is dry and edges have started to pull away from the sides of the pan, 25 to 30 minutes. Let cool completely before slicing.