Abstract The Pandoraviridae is a rapidly growing family of giant viruses, all of which have been isolated using laboratory strains of Acanthamoeba. The genomes of ten distinct strains have been fully characterized, reaching up to 2.5 Mb in size. These double-stranded DNA genomes encode the largest of all known viral proteomes and are propagated in oblate virions that are among the largest ever-described (1.2 µm long and 0.5 µm wide). The evolutionary origin of these atypical viruses is the object of numerous speculations. Applying the Chaos Game Representation to the pandoravirus genome sequences, we discovered that the tetranucleotide (4-mer) “AGCT” is totally absent from the genomes of 2 strains ( P. dulcis and P. quercus ) and strongly underrepresented in others. Given the amazingly low probability of such an observation in the corresponding randomized sequences, we investigated its biological significance through a comprehensive study of the 4-mer compositions of all viral genomes. Our results indicate that “AGCT” was specifically eliminated during the evolution of the Pandoraviridae and that none of the previously proposed host-virus antagonistic relationships could explain this phenomenon. Unlike the three other families of giant viruses (Mimiviridae, Pithoviridae, Molliviridae) infecting the same Acanthamoeba host, the pandoraviruses exhibit a puzzling genomic anomaly suggesting a highly specific DNA editing in response to a new kind of strong evolutionary pressure. Importance The recent years have seen the discovery of several families of giant DNA viruses all infecting the ubiquitous amoebozoa of the genus Acanthamoeba. With dsDNA genomes reaching 2.5 Mb in length packaged in oblate particles the size of a bacterium, the pandoraviruses are the most complex and largest viruses known as of today. In addition to their spectacular dimensions, the pandoraviruses encode the largest proportion of proteins without homolog in other organisms, thought to result from a de novo gene creation process. While using comparative genomics to investigate the evolutionary forces responsible for the emergence of such an unusual giant virus family, we discovered a unique bias in the tetranucleotide composition of the pandoravirus genomes that can only result from an undescribed evolutionary process not encountered in any other microorganism.