CRISPR/Cas9 gene editing has the potential to revolutionize the clinical management of HIV-1 infection, and may eliminate the need for antiretroviral therapy (ART). Current gene therapies attempt to either excise HIV-1 provirus or target HIV-1 entry receptors to prevent infection of new cells. Using a viral dynamic model, we determined that combining these two interventions, in the presence or absence of ART, significantly lowers the gene editing efficacy thresholds required to achieve an HIV-1 cure. To implement this dual-targeting approach, we engineered a single lentiviral vector that simultaneously targets multiple highly-conserved regions of the provirus and the host CXCR4 coreceptor, and developed a novel coculture system enabling real-time monitoring of latent infection, viral reactivation, and infection of new target cells. Simultaneous dual-targeting depleted HIV-1-infected cells with significantly greater potency than vectors targeting either virus or host independently, highlighting its potential as an HIV-1 cure strategy.