The HIV-1 capsid (CA) protein lattice encases viral genomic RNA and regulates steps essential to target-cell invasion1. Cyclophilin A (CypA) has interacted with the CA of lentiviruses related to HIV-1 for millions of years2-7. Disruption of the CA-CypA interaction decreases HIV-1 infectivity in human cells8-12 but stimulates infectivity in non-human primate cells13-15. Genetic and biochemical data suggest that CypA protects HIV-1 from a CA-specific restriction factor in human cells16-20. Discovery of the CA-specific restriction factor tripartite-containing motif 5α (TRIM5α)21 and multiple, independently derived, TRIM5-CypA fusion genes4,5,15,22-26 pointed to human TRIM5α being the CypA-sensitive restriction factor. However, HIV-1 restriction by human TRIM5α in tumour cell lines is minimal21 and inhibition of such activity by CypA has not been detected27. Here, by exploiting reverse genetic tools optimized for primary human blood cells, we demonstrate that disruption of the CA-CypA interaction renders HIV-1 susceptible to potent restriction by human TRIM5α, with the block occurring before reverse transcription. Endogenous TRIM5α associated with virion cores as they entered the cytoplasm, but only when the CA-CypA interaction was disrupted. These experiments resolve the long-standing mystery of the role of CypA in HIV-1 replication by demonstrating that this ubiquitous cellular protein shields HIV-1 from previously inapparent restriction by human TRIM5α.