Attackers and defenders of computer systems both strive to gain complete control over the system. To maximize their control, both attackers and defenders have migrated to low-level, operating system code. In this paper, we propose a new type of malicious software which gains qualitatively more control over a system. This new type of malware, which we call a hypervirus, installs a virtual-machine monitor underneath an existing operating system and hoists the original operating system into a virtual machine. Hyperviruses are hard to detect and remove because their state cannot be accessed by software running in the target system. Further, hyperviruses support general-purpose malicious services by allowing such services to run in a separate operating system that is protected from the target system. We explore this new threat by implementing two prototype hyperviruses. We use our prototype hyperviruses to subvert Windows XP and Linux target systems, and we implement four example malicious services using the hypervirus platform. Last, we use what we learn from our prototype hyperviruses to explore ways to defend against this new threat.