Phytoplankton-virus interactions are major determinants of geochemical cycles in the oceans. Viruses are responsible for the redirection of carbon and nutrients away from larger organisms back towards microorganisms via the lysis of microalgae in a process coined the "viral shunt". Virus-host interactions are generally expected to follow "boom and bust" dynamics, whereby a numerically dominant strain is lysed and replaced by a virus resistant strain. Here, we isolated a microalga and its infective nucleo-cytoplasmic large DNA virus (NCLDV) concomitantly from the environment in the surface NW Mediterranean Sea, Ostreococcus mediterraneus, and show continuous growth in culture of both the microalga and the virus. Evolution experiments through single cell bottlenecks demonstrate that, in the absence of the virus, susceptible cells evolve from one ancestral resistant single cell, and vice-versa; that is that resistant cells evolve from one ancestral susceptible cell. This provides evidence that the observed sustained viral production is the consequence of a minority of virus-susceptible cells. The emergence of these cells is explained by low-level phase switching between virus-resistant and virus-susceptible phenotypes, akin to a bet hedging strategy. Whole genome sequencing and analysis of the ~14 Mb microalga and the ~200 kb virus points towards ancient speciation of the microalga within the Ostreococcus species complex and frequent gene exchanges between prasinoviruses infecting Ostreococcus species. Re-sequencing of one susceptible strain demonstrated that the phase switch involved a large 60 Kb deletion of one chromosome. This chromosome is an outlier chromosome compared to the streamlined, gene dense, GC-rich standard chromosomes, as it contains many repeats and few orthologous genes. While this chromosome has been described in three different genera, its size increments have been previously associated to antiviral immunity and resistance in another species from the same genus. Mathematical modelling of this mechanism predicts microalga-virus population dynamics consistent with the observation of continuous growth of both virus and microalga. Altogether, our results suggest a previously overlooked strategy in phytoplankton-virus interactions.