Preheat the oven 350 F. Line a loaf pan with parchment paper.
In a bowl, add the flour, cocoa powder, baking soda, baking powder, and salt. Mix to combine. Set aside.
Using the large holes of a box grater, grate the zucchini. Add the grated zucchini to a large bowl.
Add the eggs, Greek yogurt, oil, and sugar to the bowl with the zucchini. Mix well until everything is fully incorporated.
Pour the dry ingredients into the bowl with the wet ingredients. Mix until combined, making sure not to overmix. Fold in the chocolate chips.
Pour mixture into the loaf pan (it will be thick!), using a spoon or spatula to spread it evenly and smooth it out on top.
Bake in the preheated oven for 40-45 minutes, until a knife inserted in the center comes out clean. Note that every oven is different - while 45 minutes was a good time for my oven, you may need to cook a little longer (my oven tends to run a little hot).