Preheat an oven to 325 degrees F (165 degrees C). Grease and flour a 9x13-inch pan. Combine flour, cocoa powder, baking soda, and baking powder in a bowl.
Mix the milk and vinegar in a large bowl. Let stand for 5 minutes to sour the milk. Beat in the butter, sugar, vegetable oil, eggs, and vanilla extract. Stir the liquid ingredients into the flour mixture until just combined. Fold in the zucchini. Pour batter into the prepared pan, and sprinkle with chocolate chips.
Bake in the preheated oven until a toothpick inserted into the center comes out clean, about 45 minutes. Cool in the pans for 10 minutes before removing to cool completely on a wire rack.