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Generative Adversarial Networks (GANs) have made releasing of synthetic images a viable approach to share data without releasing the original dataset. It has been shown that such synthetic data can be used for a variety of downstream tasks such as training classifiers that would otherwise require the original dataset to be shared. However, recent work has shown that the GAN models and their synthetically generated data can be used to infer the training set membership by an adversary who has access to the entire dataset and some auxiliary information. Current approaches to mitigate this problem (such as DPGAN) lead to dramatically poorer generated sample quality than the original non--private GANs. Here we develop a new GAN architecture (privGAN), where the generator is trained not only to cheat the discriminator but also to defend membership inference attacks. The new mechanism provides protection against this mode of attack while leading to negligible loss in downstream performances. In addition, our algorithm has been shown to explicitly prevent overfitting to the training set, which explains why our protection is so effective. The main contributions of this paper are: i) we propose a novel GAN architecture that can generate synthetic data in a privacy preserving manner without additional hyperparameter tuning and architecture selection, ii) we provide a theoretical understanding of the optimal solution of the privGAN loss function, iii) we demonstrate the effectiveness of our model against several white and black--box attacks on several benchmark datasets, iv) we demonstrate on three common benchmark datasets that synthetic images generated by privGAN lead to negligible loss in downstream performance when compared against non--private GANs.