We introduce a data-driven approach to aid the repairing and conservation of archaeological objects: ORGAN, an object reconstruction generative adversarial network (GAN). By using an encoder-decoder 3D deep neural network on a GAN architecture, and combining two loss objectives: a completion loss and an Improved Wasserstein GAN loss, we can train a network to effectively predict the missing geometry of damaged objects. As archaeological objects can greatly differ between them, the network is conditioned on a variable, which can be a culture, a region or any metadata of the object. In our results, we show that our method can recover most of the information from damaged objects, even in cases where more than half of the voxels are missing, without producing many errors.