This paper attempts to define what is a group and what is privacy in order to determine how a privacy right might attach to groups distinctly from the individual privacy rights of its members, and what might be the content of such a group privacy right. The challenge faced by group privacy is to enable the positive uses of Big Data while restricting the oppressive uses to the extent possible. This cannot be done by legislation or stakeholders alone; it also requires improving awareness and data literacy, and harnessing technology itself to improve data security and accountability for breaches.