Infections by the Ebola (EboV) and Marburg (MarV) filoviruses cause a rapidly fatal hemorrhagic fever in humans for which no approved antivirals are available. Filovirus entry is mediated by the viral spike glycoprotein (GP), which attaches viral particles to the cell surface, delivers them to endosomes, and catalyzes fusion between viral and endosomal membranes. Additional host factors in the endosomal compartment are likely required for viral membrane fusion. However, despite considerable efforts, these critical host factors have defied molecular identification. Here we describe a genome-wide haploid genetic screen in human cells to identify host factors required for EboV entry. Our screen uncovered 67 mutations disrupting all six members of the HOPS multisubunit tethering complex, which is involved in fusion of endosomes to lysosomes, and 39 independent mutations that disrupt the endo/lysosomal cholesterol transporter protein Niemann-Pick C1 (NPC1). Cells defective for the HOPS complex or NPC1 function, including primary fibroblasts derived from human Niemann-Pick type C1 disease patients, are resistant to infection by EboV and MarV, but remain fully susceptible to a suite of unrelated viruses. We show that membrane fusion mediated by filovirus glycoproteins and viral escape from the vesicular compartment requires the NPC1 protein, independent of its known function in cholesterol transport. Our findings uncover unique features of the entry pathway used by filoviruses and suggest potential antiviral strategies to combat these deadly agents.