Preheat oven to 350 degrees. Spray a 9x5 inch loaf pan with non-stick baking spray.
Shred the zucchini and squeeze in either a linen or paper towel to drain excess liquid, set aside.
In a large bowl, beat eggs and sugar until well blended.
Beat in the Greek yogurt and vanilla extract until blended. Set aside.
In a separate small bowl, whisk together the flour, cocoa powder, baking soda, cinnamon, salt, and baking powder.
Stir the wet ingredients into the dry ingredients to blend together. Add in the shredded zucchini and chocolate chips to combine the ingredients.
Spoon the batter into the greased loaf pan. Place in the preheated oven for about an hour. Begin to check it at 50 minutes by sticking the center of the loaf with a toothpick. The toothpick should be almost clean when it comes out of the loaf. Let it set in the loaf pan for about 10 minutes. Then remove from loaf pan and place on wire rack to cool completely!