Preheat the oven to 350°F (175°C). Line a baking sheet with parchment paper.
In a medium bowl, whisk together the flour, oats, baking soda, cinnamon, and salt.
In a large bowl, beat together the butter, brown sugar, and granulated sugar until smooth and creamy.
Add the egg and vanilla extract to the sugar mixture and beat until combined.
Stir in the grated zucchini.
Gradually add the dry ingredients to the wet ingredients, mixing just until incorporated.
Fold in the chocolate chips.
Drop tablespoon-sized balls of dough onto the prepared baking sheet, spacing them about 2 inches apart.
Bake for 10-12 minutes, or until the edges are golden brown.
Allow the cookies to cool on the baking sheet for 5 minutes before transferring them to a wire rack to cool completely.