Place a rack in the center of your oven and preheat to 325°F. Lightly coat a 9×5-inch loaf pan with nonstick spray, and line with parchment paper. Allow the two opposite sides of the parchment to overhang the edges of the pan so you can easily remove the bread later. Coat with nonstick spray once more.
Grate and measure the zucchini, then squeeze it dry with a paper towels.
In a large mixing bowl, briskly whisk together the eggs, honey, Greek yogurt, oil, and vanilla extract until smooth.
Sprinkle the cinnamon, baking soda, baking powder, and salt over the top of the batter, then stir briefly to combine.
Sprinkle the all-purpose and whole wheat flours over the top. With a rubber spatula or wooden spoon, stir just until the flour disappears.
Fold in the zucchini and chocolate chips, just until incorporated. The batter will be very thick.
Scrape the zucchini bread batter into the prepared pan and smooth the top. Decorate with a few chocolate chips.
Bake the chocolate chip zucchini bread for 50 to 60 minutes, or until a toothpick inserted into the center comes out clean (if you want to be precise, the bread should register 195° to 200°F on an instant-read thermometer).
Let cool in the pan for 10 minutes, then carefully use the parchment to lift it onto a wire rack to cool completely. Slice with a serrated knife.