Preheat oven to 350°F and line a loaf pan with parchment paper.
In a medium bowl, whisk together the flour, cocoa powder, baking soda, cinnamon and salt. Set aside.
In another large bowl beat the eggs with a hand mixer. Add the applesauce, cane sugar and oil and beat until combined.
Transfer the dry ingredients on top of the wet ingredients and mix until no streaks remain. Fold in the zucchini and the chocolate chips.
Pour the batter into the prepared pan and bake for 50-55 minutes, or until a toothpick inserted in the center of the loaf comes out clean. If necessary, tent the pan with foil after 40 minutes of baking to prevent the top from browning too much.
Remove from the oven and allow the bread to cool completely in the pan set on a wire rack before slicing.