Paramyxoviruses can establish persistent infections both in vitro and in vivo, some of which lead to chronic disease. However, little is known about the molecular events that contribute to the establishment of persistent infections by RNA viruses. Using parainfluenza virus type 5 (PIV5) as a model we show that phosphorylation of the P protein, which is a key component of the viral RNA polymerase complex, determines whether or not viral transcription and replication becomes repressed at late times after infection. If the virus becomes repressed, persistence is established, but if not, the infected cells die. We found that single amino acid changes at various positions within the P protein switched the infection phenotype from lytic to persistent. Lytic variants replicated to higher titres in mice than persistent variants and caused greater infiltration of immune cells into infected lungs but were cleared more rapidly. We propose that during the acute phases of viral infection in vivo, lytic variants of PIV5 will be selected but, as the adaptive immune response develops, variants in which viral replication can be repressed will be selected, leading to the establishment of prolonged, persistent infections. We suggest that similar selection processes may operate for other RNA viruses.