The genus Orthopoxviridae contains a diverse group of human pathogens including monkeypox, smallpox and vaccinia. These viruses are presumed to be less dependent on host functions than other DNA viruses because they have large genomes and replicate in the cytoplasm, but a detailed understanding of the host factors required by orthopoxviruses is lacking. To address this topic, we performed an unbiased, genome-wide pooled RNAi screen targeting over 17,000 human genes to identify the host factors that support orthopoxvirus infection. We used secondary and tertiary assays to validate our screen results. One of the strongest hits was heat shock factor 1 (HSF1), the ancient master regulator of the cytoprotective heat-shock response. In investigating the behavior of HSF1 during vaccinia infection, we found that HSF1 was phosphorylated, translocated to the nucleus, and increased transcription of HSF1 target genes. Activation of HSF1 was supportive for virus replication, as RNAi knockdown and HSF1 small molecule inhibition prevented orthopoxvirus infection. Consistent with its role as a transcriptional activator, inhibition of several HSF1 targets also blocked vaccinia virus replication. These data show that orthopoxviruses co-opt host transcriptional responses for their own benefit, thereby effectively extending their functional genome to include genes residing within the host DNA. The dependence on HSF1 and its chaperone network offers multiple opportunities for antiviral drug development.