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We propose a one-shot ultra-high-resolution generative adversarial network (OUR-GAN) framework that generates non-repetitive 16K (16, 384 x 8, 640) images from a single training image and is trainable on a single consumer GPU. OUR-GAN generates an initial image that is visually plausible and varied in shape at low resolution, and then gradually increases the resolution by adding detail through super-resolution. Since OUR-GAN learns from a real ultra-high-resolution (UHR) image, it can synthesize large shapes with fine details and long-range coherence, which is difficult to achieve with conventional generative models that rely on the patch distribution learned from relatively small images. OUR-GAN can synthesize high-quality 16K images with 12.5 GB of GPU memory and 4K images with only 4.29 GB as it synthesizes a UHR image part by part through seamless subregion-wise super-resolution. Additionally, OUR-GAN improves visual coherence while maintaining diversity by applying vertical positional convolution. In experiments on the ST4K and RAISE datasets, OUR-GAN exhibited improved fidelity, visual coherency, and diversity compared with the baseline one-shot synthesis models. To the best of our knowledge, OUR-GAN is the first one-shot image synthesizer that generates non-repetitive UHR images on a single consumer GPU. The synthesized image samples are presented at https://our-gan.github.io.