Generative Artificial Intelligence (AI) is boosting anticipatory forms of governance, through which state actors seek to predict the future and strategically intervene in the present. In this context, city brains represent an emerging type of generative AI currently employed in urban governance and public policy in a growing number of cities. City brains are large-scale AIs residing in vast digital urban platforms, which manage multiple urban domains including transport, safety, health, and environmental monitoring. They use Large Language Models (LLMs) to generate visions of urban futures: visions that are in turn used by policymakers to generate new urban policies. In this paper, we advance a twofold contribution. Theoretically, we develop a critical theory of anticipatory governance in the age of generative AI. More specifically, we focus on technocratic approaches to anticipatory governance, to explain how the act of governing extends into the future by means of predictive AI technology. Our approach is critical in order to expose the dangers that the use of AI (generative AI, in particular) in urban governance poses, and to identify their causes. These dangers include the formation of a policy process that, under the influence of unintelligible LLMs, risks losing transparency and thus accountability, and the marginalization of human stakeholders (citizens, in particular) as the role of AI in the management of cities keeps growing and governance begins to turn posthuman. Empirically, we critically examine an existing city brain project under development in China and ground our critical theory in a real-life example.