As AI models become more embedded in critical sectors like finance, healthcare, and the military, their inscrutable behavior poses ever-greater risks to society. To mitigate this risk, we propose Guillotine, a hypervisor architecture for sandboxing powerful AI models -- models that, by accident or malice, can generate existential threats to humanity. Although Guillotine borrows some well-known virtualization techniques, Guillotine must also introduce fundamentally new isolation mechanisms to handle the unique threat model posed by existential-risk AIs. For example, a rogue AI may try to introspect upon hypervisor software or the underlying hardware substrate to enable later subversion of that control plane; thus, a Guillotine hypervisor requires careful co-design of the hypervisor software and the CPUs, RAM, NIC, and storage devices that support the hypervisor software, to thwart side channel leakage and more generally eliminate mechanisms for AI to exploit reflection-based vulnerabilities. Beyond such isolation at the software, network, and microarchitectural layers, a Guillotine hypervisor must also provide physical fail-safes more commonly associated with nuclear power plants, avionic platforms, and other types of mission critical systems. Physical fail-safes, e.g., involving electromechanical disconnection of network cables, or the flooding of a datacenter which holds a rogue AI, provide defense in depth if software, network, and microarchitectural isolation is compromised and a rogue AI must be temporarily shut down or permanently destroyed.