Preheat oven to 350 degrees F. Grease a 9x5 inch loaf pan with nonstick spray and set aside.
Place the shredded zucchini in a clean towel or several paper towels and squeeze out excess water. Set aside.
In a large bowl, whisk together the flour, cocoa powder, baking soda, baking powder, salt and chocolate chips until mixed evenly. Set aside.
In a separate bowl, whisk together the eggs, oil, yogurt, sugar and vanilla. Slowly pour the dry ingredients into the wet ingredients and gently whisk until combined. Finally, gently fold the shredded zucchini into the batter.
Pour the batter into the prepared baking pan and bake for 45-55 minutes or until toothpick inserted comes out clean. Allow your bread to cool completely in the pan set atop a wire rack before serving.