Recent advancements in large language models (LLMs) necessitate extensive computational resources, prompting the use of diverse hardware accelerators from multiple vendors. However, traditional distributed training frameworks struggle to efficiently utilize hyper-heterogeneous clusters comprising thousands of chips due to significant disparities in software stacks, operator implementations, communication libraries, and hardware capabilities. To address these challenges, we propose H2, which stands for HyperHetero and is a systematic framework enabling efficient training of LLMs on clusters with over 1,000 heterogeneous chips. H2 incorporates DiTorch, a unified PyTorch-compatible interface ensuring program consistency across chips, and DiComm, a device-direct RDMA communication library optimized for heterogeneous environments. Furthermore, we introduce HeteroPP with HeteroAuto, an adaptive pipeline parallelism strategy that dynamically balances computational load, memory limitations, and communication overhead. Evaluations on a 100-billion-parameter LLM demonstrate that our approach consistently achieves a superlinear speedup, outperforming baseline homogeneous training solutions by up to 16.37% in our experiments. These findings validate the feasibility and efficiency of hyper-heterogeneous training at unprecedented scales.