Preheat oven to 350 degrees F. Grease a 12-cup muffin tin (or line with paper liners).
In a medium bowl, whisk together the flour, baking soda, cinnamon and salt.
In a large bowl, whisk together the sugar, eggs and vanilla extract. Using a rubber spatula, stir in the grated zucchini and the melted butter.
Add the flour mixture to the zucchini mixture and gently stir to combine. Stir in the chocolate chips until evenly distributed.
Divide the batter evenly between the muffin cups (they should be almost completely filled up). Bake until golden brown and a toothpick inserted in the center comes out clean, 20 to 25 minutes. Allow the muffins to cool in the pan for 5 minutes, then remove to a wire cooling rack and cool for an additional 30 minutes before serving. The muffins should be stored in an airtight container at room temperature for up to 4 days. You can also wrap these individually in plastic wrap, place in a freezer bag and freeze for up to 2 months.