Invention by artificial intelligence (AI) is the future of innovation. Unfortunately, as discovered through Freedom of Information Act requests, the U.S. patent regime has yet to determine how it will address patents for inventions created solely by AI (AI patents). This Article fills that void by presenting the first comprehensive analysis on the allocation of patent rights arising from invention by AI. To this end, this Article employs Coase Theorem and its corollaries to determine who should be allowed to secure these patents to maximize economic efficiency. The study concludes that letting firms using AI to create new technologies (as opposed to software companies, programmers, or downstream parties) to obtain the resulting patents is the optimal policy.