During infection by diverse viral families, RNA replication occurs on the surface of virally induced cytoplasmic membranes of cellular origin. How this process is regulated, and which cellular factors are required, has been unclear. Moreover, the host-pathogen interactions that facilitate the formation of this new compartment might represent critical determinants of viral pathogenesis, and their elucidation may lead to novel insights into the coordination of vesicular trafficking events during infection. Here we show that in Drosophila cells, Drosophila C virus remodels the Golgi apparatus and forms a novel vesicular compartment, on the surface of which viral RNA replication takes place. Using genome-wide RNA interference screening, we found that this step in the viral lifecycle requires at least two host encoded pathways: the coat protein complex I (COPI) coatamer and fatty acid biosynthesis. Our results integrate, clarify, and extend numerous observations concerning the cell biology of viral replication, allowing us to conclude that the coupling of new cellular membrane formation with the budding of these vesicles from the Golgi apparatus allows for the regulated generation of this new virogenic organelle, which is essential for viral replication. Additionally, because these pathways are also limiting in flies and in human cells infected with the related RNA virus poliovirus, they may represent novel targets for antiviral therapies.