Preheat oven to 350°F. In a large bowl, whisk together flour, xantham gum, cocoa powder, baking powder, baking soda and salt. Set aside.
In a large bowl, beat together light brown sugar, granulated sugar and eggs at medium speed until very well combined, about 3-4 minutes. With mixer still on, drizzle in vegetable oil. Add vanilla extract and beat a few seconds more.
At medium speed, slowly add the flour mixture and beat just until combined. Gently fold in the shredded zucchini and chocolate chips. Spread batter into a 9x5-inch loaf pan and smooth the top.
Bake in preheated oven for 1 hour or until a tester inserted in the middle comes out clean or with a few moist crumbs.
Cool in the pan for 15 minutes then turn out onto a wire rack to cool completely.
Notes
For a version that is not gluten free, simply omit xantham gum and use 1 1/2 cups all purpose flour.