Preheat oven to 350°. Line a large baking sheet with a Silpat baking mat or parchment paper and set aside.
In a medium bowl, whisk together flour, baking soda, and salt; set aside. Melt butter in a large saucepan over medium heat. Remove from heat; stir in cocoa powder and sugars. The mixture will be thick and resemble sand-that's ok. Add the yogurt and vanilla extract. Stir until smooth.
Add flour mixture, stirring until moist. Stir in zucchini and chocolate chips.
Drop by level tablespoons 2 inches apart onto prepared baking sheets. Bake for 10 minutes or until almost set. Cool on baking sheet for 2-3 minutes or until cookies are firm. Remove cookies from sheet and cool completely on wire racks.
Note-I squeeze the shredded zucchini in a paper towel and pat dry to remove the excess water before using.