Similar to other positive-strand RNA viruses, hepatitis C virus (HCV) causes massive rearrangements of intracellular membranes, resulting in a membranous web (MW) composed of predominantly double-membrane vesicles (DMVs), the presumed sites of RNA replication. DMVs are enriched for cholesterol, but mechanistic details on the source and recruitment of cholesterol to the viral replication organelle are only partially known. Here we focused on selected lipid transfer proteins implicated in direct lipid transfer at various endoplasmic reticulum (ER)-membrane contact sites. RNA interference (RNAi)-mediated knockdown identified several hitherto unknown HCV dependency factors, such as steroidogenic acute regulatory protein-related lipid transfer domain protein 3 (STARD3), oxysterol-binding protein-related protein 1A and -B (OSBPL1A and -B), and Niemann-Pick-type C1 (NPC1), all residing at late endosome and lysosome membranes and required for efficient HCV RNA replication but not for replication of the closely related dengue virus. Focusing on NPC1, we found that knockdown or pharmacological inhibition caused cholesterol entrapment in lysosomal vesicles concomitant with decreased cholesterol abundance at sites containing the viral replicase factor NS5A. In untreated HCV-infected cells, unesterified cholesterol accumulated at the perinuclear region, partially colocalizing with NS5A at DMVs, arguing for NPC1-mediated endosomal cholesterol transport to the viral replication organelle. Consistent with cholesterol being an important structural component of DMVs, reducing NPC1-dependent endosomal cholesterol transport impaired MW integrity. This suggests that HCV usurps lipid transfer proteins, such as NPC1, at ER-late endosome/lysosome membrane contact sites to recruit cholesterol to the viral replication organelle, where it contributes to MW functionality. A key feature of the replication of positive-strand RNA viruses is the rearrangement of the host cell endomembrane system to produce a membranous replication organelle (RO). The underlying mechanisms are far from being elucidated fully. In this report, we provide evidence that HCV RNA replication depends on functional lipid transport along the endosomal-lysosomal pathway that is mediated by several lipid transfer proteins, such as the Niemann-Pick type C1 (NPC1) protein. Pharmacological inhibition of NPC1 function reduced viral replication, impaired the transport of cholesterol to the viral replication organelle, and altered organelle morphology. Besides NPC1, our study reports the importance of additional endosomal and lysosomal lipid transfer proteins required for viral replication, thus contributing to our understanding of how HCV manipulates their function in order to generate a membranous replication organelle. These results might have implications for the biogenesis of replication organelles of other positive-strand RNA viruses.