I went through a couple of chains on my fixie bike, but I was not too happy with any of them. Basically they seemed pretty noisy when more pressure was applied where cycling.
Could you recommend one that would be both strong and quiet.
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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.
A dry and/or dirty chain is, in fact often the culprit. I've used the Sram PC7X and it was a perfectly fine, silent chain for me.
Another typical source of noise in fixed-gear or singlespeed riding is an offset chainline. Ensure your chainline offset is equal on the front and rear. Also, it is a common misconception that fixed-gear chains should be "as tight as possible", this leads to binding and premature chain wear. Lastly, I note that you're using a 1/8" chain; if you have a 3/32" chainring or cog in your drivetrain the extra 1/32" of slop can definitely cause a bit of a chattering noise.
You might want to read this chain survey. See page 44 and onwards.
Lately I have been using Dumonde lube on my chain and I have been pretty satisfied. It makes it easy to keep the drive-train clean, but it does require the chain be completely degreased prior to the first application. My experience has been consistent with the review.