Preheat your oven to 350°F. Line a 12-cup muffin tin with paper liners or lightly grease each cup.
Grate the zucchini on the large holes of a box grater. Wrap the grated zucchini in a clean kitchen towel or paper towels and press gently to remove some of the surface moisture — you want it damp, not dripping.
In a bowl whisk together the flour, baking powder, baking soda, salt, and cinnamon until evenly distributed. Set the dry mix aside.
In a separate large bowl, whisk the egg with the oil, sugar, milk, vanilla and orange zest until the sugar begins to dissolve and the mixture is smooth.
Add the dry ingredients to the wet mixture and stir with a spatula just until the batter comes together — a few small streaks of flour are okay. Avoid overmixing to keep the muffins tender.
Fold the grated zucchini and 1/3 cup of the chocolate chips into the batter until evenly distributed. Let the batter rest at room temperature for 8–10 minutes so the flour hydrates and the batter thickens slightly.
Using an ice cream scoop or two spoons, divide the batter among the prepared muffin cups, filling each about three-quarters full. Sprinkle the remaining chocolate chips over the tops.
Bake in the preheated oven for about 20–24 minutes, or until the muffin tops are golden and a toothpick inserted in the center comes out clean or with just a few moist crumbs.
Remove the pan from the oven and let the muffins cool in the tin for 6–8 minutes, then transfer to a wire rack to cool completely. Serve warm or at room temperature.