Preheat oven to 350 degrees. Prepare muffin tin by lining with silicone liners, paper liners, or greasing well.
Shred zucchini and place in colander and press down hard or squeeze excess liquid out of zucchini by placing zucchini in cheesecloth or a clean kitchen towel and squeezing firmly.
In a large mixing bowl, mix together flour, cocoa powder, baking powder, baking soda, and salt, until well combined. It is an even better idea to sift the dry ingredients together to remove any lumps from flour or cocoa powder.
In a separate mixing bowl, whisk together milk, oil, egg, applesauce and vanilla extract until well combined.
Add wet ingredients to dry ingredients and stir until just combined, careful to not over mix.
Fold zucchini and 1/3 cup chocolate chips into the batter.
Scoop out 1/4 cup batter into prepared muffin tin. Sprinkle each muffin with a couple chocolate chips if desired.
Bake for 18-22 minutes, or until toothpick inserted in middle comes out dry.