The hype over bitcoins and other cryptocurrencies has been compared to the tulip mania in seventeenth-century Netherlands. As they have gained popularity, the law has approached the subject warily, mostly from a regulatory perspective. However, there has been no comprehensive consideration of the fundamental nature of a cryptocurrency owner’s private law relation to his cryptocurrencies. Whether or not cryptocurrencies achieve mainstream adoption, this question will inevitably have to be addressed. This paper considers if bitcoins and other cryptocurrencies might be recognised as the subject of property rights by Commonwealth courts and if so, what such rights ought to entail. It begins with a consideration of the controversial question of the scope of the law of property before considering bitcoin’s place within it. It suggests that the common law adopts a more expansive view of property than civilian systems and that it is thus able to accommodate bitcoins and other cryptocurrencies within its law of property. However, owing to their unusual nature, legal rights to them must take on a unique and unorthodox form. This paper also addresses the particular challenges to the law that are posed by the code underlying bitcoin.