Since NUMA architecture has to access remote memory, the interconnection network determines the performance of the CC-NUMA system. Bus, which has been used as a popular interconnection network, has many limits in a large-scale system because of the limited physical scalability and bandwidth. The dual ring interconnection network, composed of high-speed point-to-point links, is made to resolve the defects of the bus for the large-scale system. However, it also has a problem, in that the response latency is rapidly increased when many nodes are attached to the snooping based CC-NUMA system with the dual ring. In this paper, we propose a chordal ring architecture in order to overcome the problem of the dual ring on a snooping based CC-NUMA system, and design an efficient link controller adapted to this architecture. We will also analyze the effects of chordal ring architecture on the system performance and the response latency by using a probability-driven simulator.