Researchers, supported by data from polyploid plants, have suggested that whole genome duplication (WGD) may induce genomic instability and rearrangement, an idea which could have important implications for vertebrate evolution. Benefiting from the newly released amphioxus genome sequence (Branchiostoma floridae), an invertebrate that researchers have hoped is representative of the ancestral chordate genome, we have used gene proximity conservation to estimate rates of genome rearrangement throughout vertebrates and some of their invertebrate ancestors. We find that, while amphioxus remains the best single source of invertebrate information about the early chordate genome, its genome structure is not particularly well conserved and it cannot be considered a fossilization of the vertebrate preduplication genome. In agreement with previous reports, we identify two WGD events in early vertebrates and another in teleost fish. However, we find that the early vertebrate WGD events were not followed by increased rates of genome rearrangement. Indeed, we measure massive genome rearrangement prior to these WGD events. We propose that the vertebrate WGD events may have been symptoms of a preexisting predisposition toward genomic structural change.