Nuclei segmentation is a fundamental task for various computational pathology applications, including nuclei morphology analysis, cell type classification, and cancer grading. Deep learning has emerged as a powerful approach to segmenting nuclei, but the accuracy of convolutional neural networks (CNNs) depends on the volume and quality of labeled histopathology data for training. In particular, conventional CNN-based approaches lack structured prediction capabilities, which are required to distinguish overlapping and clumped nuclei. Here, we present an approach to nuclei segmentation that overcomes these challenges by utilizing a conditional generative adversarial network (cGAN) trained with synthetic and real data. We generate a large dataset of H&E training images with perfect nuclei segmentation labels using an unpaired GAN framework. This synthetic data along with real histopathology data from six different organs are used to train a conditional GAN with spectral normalization and gradient penalty for nuclei segmentation. This adversarial regression framework enforces higher-order spacial-consistency when compared to conventional CNN models. We demonstrate that this nuclei segmentation approach generalizes across different organs, sites, patients and disease states, and outperforms conventional approaches, especially in isolating individual and overlapping nuclei.