Cut off the root ends of the zucchini and use a shredder to shred. Place it on a kitchen towel and sprinkle it with a pinch of salt. Let the shredded zucchini sit for 15 minutes. The salt will cause it to drain its liquids.
In a large bowl, combine the flour, sugar, starch, cocoa, baking powder, soda, coffee, and salt. Stir together.
In a separate bowl, stir together the oil, yogurt, vinegar, and vanilla.
Press the zucchini to remove excess lquids and use a paper towel to dry it off.
Pour the yogurt mixture in with the flour mixture and stir to combine. Add the chocolate chips and zucchini and stir until just combined.
Use a spatula to spread the batter evenly across the prepared pan. Bake for 35 to 40 minutes. Insert a tester in the middle of the cake. When it comes out clean, the cake is done. Remove from oven and set aside to cool completely before frosting.