Quiet and strong chain recommendation for fixed gear commuter bike
Chain noise is not completely avoidable on fixed-gears, due to the stress from chain tension, etc. However, there are many types of chain which would be inappropriate to use and would cause extra noise.

Be sure to purchase a 'track' chain (some are produced by Miche, Izumi, and KMC) and expect to pay $20+ for a quality chain.

Also, be sure to keep your chain clean and well lubricated! Even on regular bikes, the majority of chain noise comes from a dry chain.