Preheat the oven to 350°F (175°C). Line two baking sheets with parchment paper.
In a medium bowl, whisk together the rolled oats, all-purpose flour, baking soda, ground cinnamon, and salt.
In a large bowl, using an electric mixer, beat the softened unsalted butter, granulated sugar, and light brown sugar until creamy and smooth, about 2-3 minutes.
Add the egg and vanilla extract to the butter mixture and beat until fully combined.
Gradually add the dry ingredients to the wet ingredients and mix until just combined.
Fold in the shredded zucchini and semi-sweet chocolate chips until evenly distributed.
Drop rounded tablespoons of dough onto the prepared baking sheets, spacing them about 2 inches apart.
Bake in the preheated oven for 10 to 12 minutes, or until the edges are lightly golden but the centers remain soft.
Remove from the oven and let the cookies cool on the baking sheets for 5 minutes before transferring them to a wire rack to cool completely.