The emergence of Superchips represents a significant advancement in next-generation AI hardware. These Superchips employ a tightly coupled heterogeneous architecture that integrates GPU and CPU on the same package, which offers unprecedented computational power. However, there has been scant research investigating how LLM training benefits from this new architecture. In this work, for the first time, we study LLM training solutions based on offloading for Superchips. We observe important differences between Superchips and traditional loosely-coupled GPU-CPU architecture, which necessitate revisiting prevailing assumptions about offloading. Based on that, we present SuperOffload, a Superchip-centric offloading system that simultaneously uses Hopper GPU, Grace CPU, and NVLink-C2C interconnect more efficiently. SuperOffload accomplishes this via a combination of techniques, such as adaptive weight offloading, bucketization repartitioning, Superchip-aware casting, speculative execution, and a highly optimized Adam optimizer for Grace CPUs. Our evaluation of SuperOffload on NVIDIA GH200 demonstrates up to 2.5x throughput improvement compared to state-of-the-art offloading-based systems, enabling training of up to 25B model on a single Superchip while achieving high training throughput. We also extend SuperOffload with ZeRO-style data parallelism and DeepSpeed-Ulysses sequence parallelism, enabling training of 13B model with sequence lengths up to 1 million tokens on 8 GH200 while achieving 55% MFU.