Along the green lineage (Chlorophyta and Streptophyta), mitochondria and chloroplast are mainly uniparentally transmitted and their evolution is thus clonal. The mode of organellar inheritance in their ancestor is less certain. The inability to make clear phylogenetic inference is partly due to a lack of information for deep branching organisms in this lineage. Here, we investigate organellar evolution in the early branching green alga Ostreococcus tauri using population genomics data from the complete mitochondrial and chloro-plast genomes. The haplotype structure is consistent with clonal evolution in mitochondria, while we find evidence for recombination in the chloroplast genome. The number of recombination events in the genealogy of the chloroplast suggests that recombination, and thus biparental inheritance, is not rare. Consistent with the evidence of recombination, we find that the ratio of the number of nonsynonymous to the synonymous polymorphisms per site is lower in chloroplast than in the mitochondria genome. We also find evidence for the segregation of two selfish genetic elements in the chloroplast. These results shed light on the role of recombination and the evolutionary history of organellar inheritance in the green lineage.