Collective communication is critical to scaling large language model (LLM) training across various parallelism strategies, including data, tensor, and pipeline parallelism on GPU clusters. However, as model sizes and training scales increase, communication overhead is emerging as a major performance bottleneck. While compression is a promising mitigation strategy, existing solutions often lack user-transparency, hinder deployment and extensibility, and are not co-designed with communication algorithms. To address these limitations, we present COCCL, a high-performance collective communication library built on top of NCCL. COCCL introduces a novel programming model that can easily integrate compression into communication workflows with flexible configurability. It features a suite of compression-aware collective algorithms and runtime overlap mechanisms that mitigate error propagation and reduce computational overhead. We integrate well-established compression techniques into COCCL and tune the compression configurations during 3D-parallel training on GPT and Qwen models with up to 7 billion parameters. Using the optimal configuration (COCCL-3D), we achieve 1.24$\times$ throughput improvement while maintaining training accuracy.