Training single-view Large Reconstruction Models (LRMs) follows the fully supervised route, requiring multi-view supervision. However, the multi-view data typically comes from synthetic 3D assets, which are hard to scale further and are not representative of the distribution of real-world object shapes. To address these limitations, we introduce Real3D, the first LRM that uses single-view real images for training, benefiting from their scalability and capturing the real-world shape distribution. Real3D introduces a novel self-training framework, including unsupervised losses at the pixel- and semantic-level, enabling LRMs to learn from these single-view images without multi-view supervision. Simultaneously, to deal with the noise of real data, Real3D also presents an automatic data curation approach to gather high-quality examples that have positive impact on training. Our experiments show that Real3D consistently outperforms prior work in diverse evaluation settings that include real and synthetic data, as well as both in-domain and out-of-domain shapes.