This paper explores a series of thought experiments that postulate the existence of “artificially intelligent law.” An artificially-intelligent legal system is defined as one with three functional capacities: 1. The system has the capacity to generate legal norms. 2. The system has the capacity to apply the legal norms that it generates. 3. The system has the capacity to use deep learning to modify the legal norms that it generates. The paper then considers the question whether such a system would be desirable as a matter of legitimacy and justice. The core idea of the paper is that the key to the evaluation of artificially intelligent law is to focus on the functional capacities of the system in comparison to comparable human systems, such as regulatory agencies.