Preheat oven to 375 degrees. Place paper muffin cups in a 12-cup muffin pan.
In a medium sized bowl, stir together applesauce, Greek yogurt, eggs and vanilla until well combined and smooth.
In a separate larger mixing bowl, whisk together flour, sugar, salt, baking powder, baking soda and cocoa. Pour the yogurt mixture into the dry mixture and stir together until combined.
Stir in zucchini, then fold in chocolate chips.
Divide batter into prepared muffins cups. Dot each cup with a few chocolate chips, if desired.
Bake at 375 degrees for about 22 minutes, or until a toothpick inserted into the middle of a muffin comes out clean.
Cool in the pan for about 10 minutes before transferring muffins to a wire rack to cool completely.