Micro-algae of the genus Ostreococcus and related species of the order Mamiellales are globally distributed in the photic zone of world's oceans where they contribute to fixation of atmospheric carbon and production of oxygen, besides providing a primary source of nutrition in the food web. Their tiny size, simple cells, ease of culture, compact genomes and susceptibility to the most abundant large DNA viruses in the sea render them attractive as models for integrative marine biology. In culture, spontaneous resistance to viruses occurs frequently. Here, we show that virus-producing resistant cell lines arise in many independent cell lines during lytic infections, but over two years, more and more of these lines stop producing viruses. We observed sweeping over-expression of all genes in more than half of chromosome 19 in resistant lines, and karyotypic analyses showed physical rearrangements of this chromosome. Chromosome 19 has an unusual genetic structure whose equivalent is found in all of the sequenced genomes in this ecologically important group of green algae.