Preheat the oven to 350°F. Lightly grease a 9-inch by 5-inch loaf pan and set aside.
In a large mixing bowl, whisk together the flour, baking soda, baking powder, salt and cinnamon. Set aside.
In a small bowl, mash the peeled banana with a fork until it's soft and gloopy.
In a large mixing bowl, combine the vegetable oil, granulated sugar, brown sugar, egg, vanilla extract, and mashed banana. Mix until it's well-combined. Set aside.
Using the smallest holes on a box grater, shred the zucchini. Squeeze the shredded zucchini in your hands to drain as much moisture as possible from it.
Add the dry ingredients into the wet ingredients and gently mix just until there is no dry flour visible. (Don't overmix, which can cause your loaf to sink in the middle as it bakes.)
Gently fold in the shredded zucchini and chocolate chips.
Pour the batter into the prepared loaf pan. Bake for 50 to 60 minutes, until a toothpick inserted into the center of the bread comes out clean. If the top starts to get really brown before the loaf is done baking, cover it with tin foil to prevent it from getting too crispy.