Preheat your oven to 350°F. Prepare a baking sheet with parchment paper or a silicone mat and set it aside.
In a medium-sized bowl, blend the flour, baking soda, salt, and cinnamon together. Set this mixture aside.
In a large mixing bowl, beat together the softened butter and both sugars using a hand mixer on medium speed until the mixture is smooth and creamy.
Incorporate the egg and vanilla extract into the butter mixture, followed by the shredded zucchini. Mix until everything is well blended.
Gradually add the dry flour mixture to the wet ingredients, stirring just until combined. Fold in the oats and chocolate chips.
Using a medium cookie scoop, drop dough portions onto the prepared baking sheet, spacing them about 2 inches apart. If desired, press a few extra chocolate chips into the tops of the dough balls.
Bake the cookies for 12-15 minutes, or until they are golden brown. Allow the cookies to cool completely on wire racks after removing them from the baking sheet.