Preheat the oven to 350°F.
Grate the zucchini coarsely and squeeze out any excess moisture using a clean kitchen towel.
Whisk together the melted butter, brown sugar, egg, and vanilla extract until smooth.
In a separate bowl, combine the flour, oats, baking powder, and salt.
Add the dry ingredients to the wet ingredients and stir until just combined. Quickly fold in the zucchini and chocolate chips.
Chill the dough for about 30 minutes.
Drop the dough by teaspoonfuls onto a baking sheet lined with parchment paper, forming small mounds.
Bake for about 10 minutes, or until the edges are lightly golden brown.