Preheat the oven to 350°F; spray 9 x 5-inch pan with nonstick spray or line with parchment paper.
In a large mixing bowl, beat the eggs, honey, oil, sugar, and vanilla until smooth.
In medium mixing bowl, whisk together salt, baking soda, baking powder, cocoa, and flour. Add to egg mixture, mixing until well combined.
Stir in the zucchini and chocolate chips.
Pour the batter into the prepared pan.
Bake the bread for 65 to 75 minutes, until the loaf tests done (a toothpick or cake tester inserted into the center will come out clean except for a light smear of chocolate from the melted chips). Shield top of bread with aluminum foil to prevent over browning during last 10 minutes of baking time if needed.
Remove the bread from the oven, and let it cool for 10 to 15 minutes before turning it out of the pan onto a rack.
Cool completely before slicing; store well-wrapped, at room temperature.
To make the optional drizzle: Melt 1/2 cup of chocolate chips at medium power in the microwave; drizzle over the top of the cooled bread.