The efficiency of Bayesian optimization (BO) in chemistry is often hindered by sparse experimental data and complex reaction mechanisms. To overcome these limitations, we introduce ChemBOMAS, a new framework named LLM-Enhanced Multi-Agent System for accelerating BO in chemistry. ChemBOMAS's optimization process is enhanced by LLMs and synergistically employs two strategies: knowledge-driven coarse-grained optimization and data-driven fine-grained optimization. First, in the knowledge-driven coarse-grained optimization stage, LLMs intelligently decompose the vast search space by reasoning over existing chemical knowledge to identify promising candidate regions. Subsequently, in the data-driven fine-grained optimization stage, LLMs enhance the BO process within these candidate regions by generating pseudo-data points, thereby improving data utilization efficiency and accelerating convergence. Benchmark evaluations** further confirm that ChemBOMAS significantly enhances optimization effectiveness and efficiency compared to various BO algorithms. Importantly, the practical utility of ChemBOMAS was validated through wet-lab experiments conducted under pharmaceutical industry protocols, targeting conditional optimization for a previously unreported and challenging chemical reaction. In the wet experiment, ChemBOMAS achieved an optimal objective value of 96%. This was substantially higher than the 15% achieved by domain experts. This real-world success, together with strong performance on benchmark evaluations, highlights ChemBOMAS as a powerful tool to accelerate chemical discovery.