Preheat the oven to 350°F (175°C). Grease a 9×5-inch loaf pan and set aside.
In a medium bowl, whisk together the all-purpose flour, unsweetened cocoa powder, baking soda, baking powder, and salt until well combined.
In a large bowl, whisk the granulated sugar, plain Greek yogurt, vegetable oil, eggs, and vanilla extract until smooth and creamy.
Add the dry ingredients to the wet ingredients and gently fold together until just combined. Do not overmix.
Fold in the grated zucchini and mini chocolate chips until evenly distributed throughout the batter.
Pour the batter into the prepared loaf pan and spread it out evenly.
Bake in the preheated oven for 50 to 55 minutes, or until a toothpick inserted into the center comes out clean or with a few moist crumbs.
Remove the bread from the oven and let it cool in the pan for 10 minutes.
Transfer the bread to a wire rack to cool completely before slicing and serving.