Preheat the oven to 325°F. Butter a 9- by 9-inch cake pan.
Sift the flour, cocoa powder, baking soda, baking powder, and 3/4 teaspoon salt into a bowl. Combine the sugar, butter, oil, eggs, and vanilla in another large bowl. Using an electric mixer, beat the ingredients on medium-high for 2 minutes, until well blended. Alternately add the dry mixture and the sour cream to the egg mixture, blending after each on low speed. Add the zucchini and mix gently. Pour into prepared pan.
Bake for 60 to 70 minutes (for 9-inch pan, or 40 minutes for 9×13-inch pan), until a tester inserted into the center of the cake comes out clean. Cool.
For glaze, heat cream in a small saucepan, add chips. Remove from heat and let stand 1 minute, whisk until smooth. Drizzle over cake.
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