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Generative Adversarial Networks (GAN) have many potential medical imaging applications, including data augmentation, domain adaptation, and model explanation. Due to the limited memory of Graphical Processing Units (GPUs), most current 3D GAN models are trained on low-resolution medical images, these models either cannot scale to high-resolution or are prone to patchy artifacts. In this work, we propose a novel end-to-end GAN architecture that can generate high-resolution 3D images. We achieve this goal by using different configurations between training and inference. During training, we adopt a hierarchical structure that simultaneously generates a low-resolution version of the image and a randomly selected sub-volume of the high-resolution image. The hierarchical design has two advantages: First, the memory demand for training on high-resolution images is amortized among sub-volumes. Furthermore, anchoring the high-resolution sub-volumes to a single low-resolution image ensures anatomical consistency between sub-volumes. During inference, our model can directly generate full high-resolution images. We also incorporate an encoder with a similar hierarchical structure into the model to extract features from the images. Experiments on 3D thorax CT and brain MRI demonstrate that our approach outperforms state of the art in image generation. We also demonstrate clinical applications of the proposed model in data augmentation and clinical-relevant feature extraction.