Preheat the oven to 325 degrees F (165 degrees C). Grease and flour two 8X4-inch loaf pans.

Beat eggs in a large bowl until light and foamy. Mix in shredded zucchini, sugar, oil, and vanilla until thoroughly combined.

Whisk flour, cocoa powder, salt, baking soda, and baking powder together in a separate bowl; stir into zucchini mixture. Mix in nuts and chocolate chips. Pour batter into the prepared loaf pans.

Bake in the preheated oven until a toothpick inserted into the center of loaves comes out clean, about 1 hour. Let loaves sit in the pans for 10 minutes before removing to a wire rack to cool completely.