We propose OUR-GAN, the first one-shot ultra-high-resolution (UHR) image synthesis framework that generates non-repetitive images with 4K or higher resolution from a single training image. OUR-GAN generates a visually coherent image at low resolution and then gradually increases the resolution by super-resolution. Since OUR-GAN learns from a real UHR image, it can synthesize large-scale shapes with fine details while maintaining long-range coherence, which is difficult with conventional generative models that generate large images based on the patch distribution learned from relatively small images. OUR-GAN applies seamless subregion-wise super-resolution that synthesizes 4k or higher UHR images with limited memory preventing discontinuity at the boundary. Additionally, OUR-GAN improves diversity and visual coherence by adding vertical positional embeddings to the feature maps. In experiments on the ST4K and RAISE datasets, OUR-GAN exhibited improved fidelity, visual coherency, and diversity compared with existing methods. The synthesized images are presented at https://anonymous-62348.github.io.