Communication has emerged as a critical bottleneck in the distributed training of large language models (LLMs). While numerous approaches have been proposed to reduce communication overhead, the potential of lossless compression has remained largely underexplored since compression and decompression typically consume larger overheads than the benefits of reduced communication traffic. We observe that the communication data, including activations, gradients and parameters, during training often follows a near-Gaussian distribution, which is a key feature for data compression. Thus, we introduce ZipCCL, a lossless compressed communication library of collectives for LLM training. ZipCCL is equipped with our novel techniques: (1) theoretically grounded exponent coding that exploits the Gaussian distribution of LLM tensors to accelerate compression without expensive online statistics, (2) GPU-optimized compression and decompression kernels that carefully design memory access patterns and pipeline using communication-aware data layout, and (3) adaptive communication strategies that dynamically switch collective operations based on workload patterns and system characteristics. Evaluated on a 64-GPU cluster using both mixture-of-experts and dense transformer models, ZipCCL reduces communication time by up to 1.35$\times$ and achieves end-to-end training speedups of up to 1.18$\times$ without any impact on model quality.