Conditional generative models enjoy significant progress over the past few years. One of the popular conditional models is Auxiliary Classifier GAN (AC-GAN) that generates highly discriminative images by extending the loss function of GAN with an auxiliary classifier. However, the diversity of the generated samples by AC-GAN tends to decrease as the number of classes increases. In this paper, we identify the source of low diversity issue theoretically and propose a practical solution to the problem. We show that the auxiliary classifier in AC-GAN imposes perfect separability, which is disadvantageous when the supports of the class distributions have significant overlap. To address the issue, we propose Twin Auxiliary Classifiers Generative Adversarial Net (TAC-GAN) that adds a new player that interacts with other players (the generator and the discriminator) in GAN. Theoretically, we demonstrate that our TAC-GAN can effectively minimize the divergence between generated and real data distributions. Extensive experimental results show that our TAC-GAN can successfully replicate the true data distributions on simulated data, and significantly improves the diversity of class-conditional image generation on real datasets.