Preheat oven to 350F. Grease a standard loaf pan (8 1/2 x 4 1/2 inch) with non-stick cooking spray and set to the side.
In a medium sized mixing bowl, whisk together yogurt, sugar, applesauce, eggs, oil and vanilla until well blended. Stir in the zucchini. Set aside.
In a large bowl, whisk together flour, cocoa, baking powder, baking soda, and salt until well blended. Fold in the chocolate chips.
Add the wet ingredients to the dry ingredients and stir until just combined and all of the dry ingredients are moistened. Do not overmix. Pour evenly into loaf pan.
Bake for 60 minutes or until a wooden pick inserted in the middle comes out clean. Cool for 5 minutes and then remove and cool on a wire rack.