Heat the oven to 325 degrees. In a mixing bowl, cream together the sugars, butter and oil. Add the eggs, vanilla extract and buttermilk and stir well to mix.
In a separate bowl, mix together the flour, cocoa, baking soda, allspice, cinnamon and salt. Stir the flour mixture into the egg mixture until well combined. Fold in the grated zucchini and chocolate chips.
Turn the batter into two greased and floured 9-inch baking pans. Bake for 25 to 30 minutes or until done. Let cool and then frost with 3 1/2 to 4 cups of your favorite icing. Serves 12.