Preheat oven to 350°F. Grease a 9-by-5-inch loaf pan with nonstick cooking spray.
In a large bowl, whisk together the flour, brown sugar, cocoa powder, baking soda, and salt.
Add the eggs, apple sauce, vanilla extract. Stir until ingredients are wet, do not over mix.
Stir in the shredded zucchini and 3/4 cup of the chocolate chips until just combined.
Pour batter into prepared pan. Sprinkle the remaining 1/4 cup of chocolate chips over the top of the bread. Bake for 50-60 minutes, or until a toothpick inserted into the center of the bread comes out mostly clean.
Remove from oven and set on cooling rack and let the bread cool in the pan for 15 minutes. Remove bread from pan and let cool completely before serving.