Heat the oven to 350°F (175°C). Grease the loaf pan and line with a parchment sling. Wash and trim the zucchini before grating.
Grate zucchini through medium holes and blot lightly with a clean towel. Remove surface water without wringing it bone-dry, then measure the prepared quantity.
Whisk flour, baking soda, salt, and cinnamon. In a separate bowl whisk brown sugar, eggs, oil, yogurt, and vanilla until smooth.
Stir grated zucchini into the wet mixture. Fold in the dry ingredients gently until only a few small flour streaks remain.
Fold in chocolate chips to finish combining. Scrape the batter into the pan and level the top without packing it down.
Bake 50–60 minutes until a skewer in the center comes out with moist crumbs but no raw batter. Avoid mistaking melted chocolate for uncooked batter.
If the crust darkens early, tent loosely with foil. Cool in the pan 15 minutes, then lift onto a rack and cool fully, about 1 hour.
Slice with a serrated knife once the loaf has settled. Cool all portions before wrapping so trapped steam does not make the zucchini-rich crumb gummy.