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Chaos is generic in strongly-coupled recurrent networks of model neurons, and thought to be a common dynamical regime in the brain. While neural chaos is typically seen as an impediment to be overcome, we show how such chaos might play a functional role in allowing the brain to learn and sample from generative models of the world. The ability to build such generative models is thought to be crucial to flexible intelligence. We construct model architectures that combine classic models of neural chaos with canonical generative modeling architectures and show that they have a number of appealing properties, including easy biologically-plausible control of sampling rates.