Many eukaryotic organisms have symbiotic associations with obligate intracellular bacteria. The clonal transmission of endosymbionts between host generations should lead to the irreversible fixation of slightly deleterious mutations in their non-recombinant genome by genetic drift. However, the stability of endosymbiosis indicates that some mechanism is involved in the amelioration of the effects of these mutations. We propose that the chaperone GroEL was involved in the acquisition of an endosymbiotic lifestyle not only by means of its over-production, as proposed by Moran, but also by its adaptive evolution mediated by positive selection to improve the interaction with the unstable endosymbiont proteome.