Since the eradication of smallpox was declared in 1980, debate has ensued over what to do with the remaining stocks of the causative agent, variola virus. For more than three decades the World Health Organization has resolved to destroy the virus isolates, now maintained in high-security laboratories in the Russian Federation and the United States, and each time the deadline has been deferred. The legal facets of this debate have been largely overlooked. As genetic resources, all viruses fall within the scope of the United Nations’ Convention on Biological Diversity (CBD) that provides for “the fair and equitable sharing of the benefits arising out of the utilisation of genetic resources”. This article examines the possible ownership scenarios for variola viruses and concludes that the conservation principles of the CBD and the ambiguous sovereign status of individual isolates may preclude the destruction of the world’s remaining variola stocks.