Latent viral infection is a persistent cause of human disease. Although standard antiviral therapies can suppress active viral replication, no existing treatment can effectively eradicate latent infection and therefore a cure is lacking for many prevalent viral diseases. The prokaryotic immune system clustered regularly interspaced short palindromic repeat (CRISPR)/Cas evolved as a natural response to phage infections, and we demonstrate here that the CRISPR/Cas9 system can be adapted for antiviral treatment in human cells by specifically targeting the genomes of latent viral infections. Patient-derived cells from a Burkitt’s lymphoma with latent Epstein–Barr virus infection showed dramatic proliferation arrest and a concomitant decrease in viral load after exposure to a CRISPR/Cas9 vector targeted to the viral genome.