Generative Adversarial Networks (GANs) are a class of artificial neural network that can produce realistic, but artificial, images that resemble those in a training set. In typical GAN architectures these images are small, but a variant known as Spatial-GANs (SGANs) can generate arbitrarily large images, provided training images exhibit some level of periodicity. Deep extragalactic imaging surveys meet this criteria due to the cosmological tenet of isotropy. Here we train an SGAN to generate images resembling the iconic Hubble Space Telescope eXtreme Deep Field (XDF). We show that the properties of 'galaxies' in generated images have a high level of fidelity with galaxies in the real XDF in terms of abundance, morphology, magnitude distributions and colours. As a demonstration we have generated a 7.6-billion pixel 'generative deep field' spanning 1.45 degrees. The technique can be generalised to any appropriate imaging training set, offering a new purely data-driven approach for producing realistic mock surveys and synthetic data at scale, in astrophysics and beyond.