RNA viruses are a major human health threat. The life cycles of many highly pathogenic RNA viruses like influenza A virus (IAV) and Lassa virus depends on host mRNA, because viral polymerases cleave 5'-m7G-capped host transcripts to prime viral mRNA synthesis ("cap-snatching"). We hypothesized that start codons within cap-snatched host transcripts could generate chimeric human-viral mRNAs with coding potential. We report the existence of this mechanism of gene origination, which we named "start-snatching." Depending on the reading frame, start-snatching allows the translation of host and viral "untranslated regions" (UTRs) to create N-terminally extended viral proteins or entirely novel polypeptides by genetic overprinting. We show that both types of chimeric proteins are made in IAV-infected cells, generate T cell responses, and contribute to virulence. Our results indicate that during infection with IAV, and likely a multitude of other human, animal and plant viruses, a host-dependent mechanism allows the genesis of hybrid genes.