Set your oven rack to the 2nd level position and preheat your oven to 325ºF.
Spray your 3, 6 inch cake pans with a flour-based baking spray. Place a circle of parchment paper in the bottom of each pan, then lightly respray. Alternatively, you can grease the pans with butter and coat in flour, but it's important to still add in the parchment paper circles (it helps to release the cake from the pan).
In a separate bowl, whisk together the all-purpose flour, unsweetened cocoa powder, and baking soda. Set to the side.
Using your hand mixer or stand mixer fitted with a paddle attachment cream the unsalted butter, vegetable shortening, vegetable oil, and granulated sugar together on medium-high speed until well blended.
Add in the egg, vanilla extract, and sour milk.
Switching your mixer speed to low, gradually add in the whisked dry ingredients and mix until just combined. Add in the shredded zucchini.
Fold in the chocolate chips.
Evenly distribute the cake batter into each 6 inch prepared cake pan, then place in the oven to bake for 45-50 minutes at 325ºF or until an inserted toothpick comes out clean from the center of each cake.
Cool cakes in the pans for 10 minutes, then carefully invert to cool completely on wire cooling racks.