Very soon, millions of AI agents will proliferate across the economy, autonomously taking billions of actions. Inevitably, things will go wrong. Humans will be defrauded, injured, even killed. Law will somehow have to govern the coming wave. But when an AI causes harm, the first question to answer, before anyone can be held accountable is: Which AI Did It? Identifying AIs is unusually difficult. AIs lack bodies. They can copy, split, merge, swarm, and vanish at will. Even today, a "single" AI agent is often an ensemble of instances based on multiple models. The complexity will only multiply as AI capabilities improve. This Article is the first to comprehensively diagnose the legal problem of identifying AIs. Two kinds of identity are required: "thin" and "thick." Thin identification ties every AI action to some human principal, essential for holding accountable the humans who make and use AI agents. Thick identification distinguishes between AI agents, qua agents -- sorting millions of AI entities into discrete, persistent units with stable, coherent goals, essential where principal-agent problems prevent humans from perfectly controlling AIs. This Article also presents a solution: the "Algorithmic Corporation" or "A-corp" -- a legal-fictional entity that can hold property, make contracts, and litigate in its own name. Owned by humans but run by AIs, A-corps solve the thin identity problem by tying AI actions to a human owner, and the thick identity problem via emergent self-organization. A-corps own the resources -- including compute -- that AIs need to accomplish their goals, giving AI managers strong incentives to share control only with goal-aligned AIs. In equilibrium, incentive and selection mechanisms force A-corps to self-organize into persistent, legally legible entities with coherent goals that respond rationally to legal incentives, like liability.