Abstract: The World Health Organization has declared the present Zika virus epidemic to be a ‘Public Health Emergency of International Concern’. The virus appears to have spread from Thailand to French Polynesia in 2013, and has since infected over a million people in the countries of South and Central America. In most cases the infection is mild and transient, but the virus does appear to be strongly neurotropic and the presumptive cause of both birth defects in fetuses and Guillain-Barré syndrome in some adults. In this paper, the techniques and utilities developed in the study of mitochondrial DNA were applied to the Zika virus. As a result, it is possible to show in a simple manner how a phylogenetic tree may be constructed and how the mutation rate of the virus can be measured. The study showed the mutation rate to vary between 12 and 25 bases a year, in a viral genome of 10272 bases. This rapid mutation rate will enable the geographic spread of the epidemic to be monitored easily and may also prove useful in assisting the identification of preventative measures that are working, and those that are not.