Preheat oven to 375°F (190°C). Line 6 standard muffin cups with paper liners or grease the cups if you prefer.
Whisk together the flour, brown sugar, baking powder, baking soda, cinnamon, and salt. Make a well in the center of the mixture.
Combine the cooled butter and the egg. Add to the well in the flour mixture, and mix just until combined.
Fold in the zucchini and chocolate chips.
Divide the batter evenly among the prepared muffin cups, using about 3 tablespoons of batter per cup to fill each cup about 3/4 full.
Bake 20 to 25 minutes, or until a pick inserted into the center comes out clean. Cool in the pan for 5-10 minutes, and then transfer the muffins to a wire rack to cool completely.