Preheat the oven to 350 F, and line a loaf pan with a piece of parchment paper so the paper hangs over two sides. This is called a parchment paper "sling", and makes it much easier to lift the bread out of the pan after baking.
In a saucepan, melt the butter over medium heat. Remove from the heat and add the chopped chocolate. Let stand for 2 minutes, then stir until smooth.
In a large bowl, whisk together the melted butter and chocolate with the sugar, buttermilk, eggs and vanilla. Stir in the grated zucchini.
Separately, sift together the flour, cocoa powder, baking powder and salt. Add the dry ingredients and 1/4 cup of the chocolate chips to the wet ingredients, and use a spatula to fold everything together just until moistened.
Spread the batter into the prepared loaf pan. Sprinkle the remaining 1/4 cup chocolate chips on top of the batter.
Bake the bread on the center oven rack for about 50-55 minutes, or until a cake tester or sharp knife inserted in the center comes out clean or with moist crumbs clinging to it.
Cool the bread in the pan for 30 minutes, then lift the bread out of the pan (by lifting up the paper overhang), and set on a cooling rack. Cool for 2 hours before slicing.