We propose a rejection sampling scheme using the discriminator of a GAN to approximately correct errors in the GAN generator distribution. We show that under quite strict assumptions, this will allow us to recover the data distribution exactly. We then examine where those strict assumptions break down and design a practical algorithm—called Discriminator Rejection Sampling (DRS)—that can be used on real data-sets. Finally, we demonstrate the efficacy of DRS on a mixture of Gaussians and on the state of the art SAGAN model. On ImageNet, we train an improved baseline that increases the best published Inception Score from 52.52 to 62.36 and reduces the Frechet Inception Distance from 18.65 to 14.79. We then use DRS to further improve on this baseline, improving the Inception Score to 76.08 and the FID to 13.75.