Host molecular chaperones are reported to facilitate the replication of flaviviruses such as dengue virus (DENV). Here, Taguwa et al. show that cytosolic heat shock protein 70 (HSP70) isoforms and their DNAJ cofactors facilitate multiple steps of the DENV life cycle, including viral entry, RNA replication and virion biogenesis. The allosteric HSP70 inhibitor JG40 potently inhibited replication of different DENV serotypes as well as other flaviviruses in primary cultures of human blood cells, without signs of viral resistance or host cell toxicity.