We present CryoGAN, a new paradigm for single-particle cryo-electron microscopy (cryo-EM) reconstruction based on unsupervised deep adversarial learning. In single-particle cryo-EM, the structure of a biomolecule needs to be reconstructed from a large set of noisy tomographic projections with unknown orientations. Current reconstruction techniques are based on a marginalized maximum-likelihood formulation that requires calculations over the set of all possible poses for each projection image, a computationally demanding procedure. Our approach is to seek a 3D structure that has simulated projections that match the real data in a distributional sense, thereby sidestepping pose estimation or marginalization. We prove that, in an idealized mathematical model of cryo-EM, this approach results in recovery of the correct structure. Motivated by distribution matching, we propose CryoGAN, a specialized GAN that consists of a 3D structure, a cryo-EM physics simulator, and a discriminator neural network. During reconstruction, the 3D structure is optimized so that its projections obtained through the simulator resemble real data (to the discriminator). Simultaneously, the discriminator is trained to distinguish real projections from simulated projections. CryoGAN takes as input only real projection images and the distribution of the cryo-EM imaging parameters. It involves neither prior training nor an initial estimation of the 3D structure. CryoGAN currently achieves a 10.8 angstrom resolution on a realistic synthetic dataset. Preliminary results on experimental beta-galactosidase and 80S ribosome data demonstrate the ability of CryoGAN to exploit data statistics under standard experimental imaging conditions. We believe that this paradigm opens the door to a family of novel likelihood-free algorithms for cryo-EM reconstruction.