Recently, various deep learning approaches have yielded highly promising results in demographic inference. One of these — Generative Adversarial Networks (GANs) — is particularly useful for mimicking real data while exploring the joint probability distribution of parameters that produce such data. In a GAN, two neural networks – known as the Discriminator and the Generator – compete in a zero-sum game, to both mimic the input data and learn about the process that generated it. However, standard simulation engines cannot be readily incorporated as GAN generators. Here we develop a GAN that is coupled with a Markov Chain Monte Carlo (MCMC) algorithm, and thus allows for inference from the full posterior probability distribution of the parameters.