Virus-microbe interactions in the ocean are commonly described by “boom and bust” dynamics, whereby a numerically dominant microorganism is lysed and replaced by a virus-resistant one. Here, we isolated a microalga strain and its infective dsDNA virus whose dynamics are characterized instead by parallel growth of both the microalga and the virus. Experimental evolution of clonal lines revealed that this viral production originates from the lysis of a minority of virus-susceptible cells, which are regenerated from resistant cells. Whole-genome sequencing demonstrated that this resistant-susceptible switch involved a large deletion on one chromosome. Mathematical modeling explained how the switch maintains stable microalga-virus population dynamics consistent with their observed growth pattern. Comparative genomics confirmed an ancient origin of this “accordion” chromosome despite a lack of sequence conservation. Together, our results show how dynamic genomic rearrangements may account for a previously overlooked coexistence mechanism in microalgae-virus interactions.