Preheat oven to 350 degrees. Generously coat a 9" x 5" loaf pan with non-stick cooking spray.
In large bowl beat eggs with an electric hand mixer. Add sugar and beat for a minute or two until completely combined. Pour in the oil, with beaters running, and then add vanilla.
In a separate bowl, whisk together the flour, cocoa powder, salt, baking powder, and baking soda. Using a wooden spoon, add dry mixture to the wet mixture in increments, alternating with the Greek yogurt, stirring after each addition. Stir in the shredded zucchini and chocolate chips.
Spoon the batter into the prepared loaf pan and smooth surface evenly. Bake for 55 to 60 minutes, or until a toothpick inserted in center comes out clean. Remove the pan from oven and allow cool for about 10 minutes. Remove bread from pan and allow to cool completely before slicing.