Preheat the oven to 350ºF (180ºC). Grease and flour a 13x9x2 inch (33cm x 23cm x 5 cm) baking pan and set it aside.
In a large mixing bowl combine the flour, sugar, cocoa powder, baking soda, baking powder, cinnamon and salt. Stir to combine well. Add the oil, milk, softened butter and vanilla. Beat with an electric mixer on low speed until combined. Add the eggs, chocolate chips and shredded zucchini and beat on medium to high speed for 2 minutes.
Spread the batter into the prepared pan. Bake in the preheated oven for about 35 minutes or until the cake tests done. Let the cake cool in the pan on a wire rack.
Sprinkle with powdered sugar if desired.
For added nutritional value and a nice crunch add 1/2 cup chopped walnuts or pecans to the cake. Add them when you add the chocolate chips and zucchini.