Hepatitis C virus (HCV) infection is characterized by persistent replication of a complex mixture of viruses termed a “quasispecies.” Transmission is generally associated with a stringent population bottleneck characterized by infection by limited numbers of “transmitted/founder” (T/F) viruses. Characterization of T/F genomes of human immunodeficiency virus type 1 (HIV-1) has been integral to studies of transmission, immunopathogenesis, and vaccine development. Here, we describe the identification of complete T/F genomes of HCV by single-genome sequencing of plasma viral RNA from acutely infected subjects. A total of 2,739 single-genome-derived amplicons comprising 10,966,507 bp from 18 acute-phase and 11 chronically infected subjects were analyzed. Acute-phase sequences diversified essentially randomly, except for the poly(U/UC) tract, which was subject to polymerase slippage. Fourteen acute-phase subjects were productively infected by more than one genetically distinct virus, permitting assessment of recombination between replicating genomes. No evidence of recombination was found among 1,589 sequences analyzed. Envelope sequences of T/F genomes lacked transmission signatures that could distinguish them from chronic infection viruses. Among chronically infected subjects, higher nucleotide substitution rates were observed in the poly(U/UC) tract than in envelope hypervariable region 1. Fourteen full-length molecular clones with variable poly(U/UC) sequences corresponding to seven genotype 1a, 1b, 3a, and 4a T/F viruses were generated. Like most unadapted HCV clones, T/F genomes did not replicate efficiently in Huh 7.5 cells, indicating that additional cellular factors or viral adaptations are necessary for in vitro replication. Full-length T/F HCV genomes and their progeny provide unique insights into virus transmission, virus evolution, and virus-host interactions associated with immunopathogenesis. IMPORTANCE Hepatitis C virus (HCV) infects 2% to 3% of the world's population and exhibits extraordinary genetic diversity. This diversity is mirrored by HIV-1, where characterization of transmitted/founder (T/F) genomes has been instrumental in studies of virus transmission, immunopathogenesis, and vaccine development. Here, we show that despite major differences in genome organization, replication strategy, and natural history, HCV (like HIV-1) diversifies essentially randomly early in infection, and as a consequence, sequences of actual T/F viruses can be identified. This allowed us to capture by molecular cloning the full-length HCV genomes that are responsible for infecting the first hepatocytes and eliciting the initial immune responses, weeks before these events could be directly analyzed in human subjects. These findings represent an enabling experimental strategy, not only for HCV and HIV-1 research, but also for other RNA viruses of medical importance, including West Nile, chikungunya, dengue, Venezuelan encephalitis, and Ebola viruses.