Preheat oven to 350 degrees F or 180 degrees C.
Shred the zucchini with skin using a box grater or food processor—no need to squeeze out the water from the zucchini. Keep aside.
In a medium-sized bowl, mix dry ingredients first the flour, cocoa powder, baking powder, baking soda, sugar, and salt until well combined.
Next, add the wet ingredients like shredded zucchini, yogurt, oil, vanilla extract, and with the help of a spatula, mix gently till everything looks combined.
If the bread mixture is dry, the water content in the zucchini will make it moist in 2-3 minutes.
Fold in ½ cup of chocolate chips. Reserve the remaining chocolate chips to sprinkle on the top.
Pour the batter into a parchment-lined and greased 9 x 5 pan and sprinkle the remaining ½ cup chocolate chips on the top of the batter.
Bake on the center rack for 40 minutes or until a toothpick inserted into the center of the bread comes out clean.
Let it cool completely, remove the bread from the pan, and allow it to cool for another 15-20 minutes before slicing.