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Perovskites are one of the most studied classes of materials, with a variety of applications in diverse fields of science and technology. Their basic composition is ABX3, where X is a nonmetal normally from the VIA or VIIA group. In this article we investigate the possibility of the existence of perovskites with X = N. Our approach is based on a combination of high-throughput techniques and global structural prediction methods. We find 21 new compositions of the form ABN3 that are thermodynamically stable (considering all possible decomposition channels) and that have therefore excellent chances of being experimentally accessible. Most of these materials crystallize in monoclinic phases, but three compounds, namely, LaReN3, LaWN3, and YReN3, are predicted to have distorted perovskite structures in their ground state. In particular, LaWN3 is a semiconductor and displays a large ferroelectric polarization. The addition of nitride compounds to the perovskite family poses numerous questions related to the chemistry of this interesting family of materials.