In a medium bowl, cream butter and sugar until fluffy. Stir in the egg and vanilla, mix well, then stir in the shredded zucchini. Sift together the flour, baking soda and cinnamon, stir into the zucchini mixture. Finally, stir in the oats, and chocolate chips.
Drop dough from a teaspoon onto an unprepared cookie sheet. Leave at least 2 inches between cookies. Bake for 10 to 12 minutes in the preheated oven. The cookies will stay soft and moist because of the zucchini.