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If you don't have the commercial products there are other options with most acids from a lemon to drain cleaners.Try soaking in white vinegar overnight for a safe home-grown approach , or a stronger acid like oxalic acid for twenty minutes or so if you have either. Then loosened rust may be abraded away with wire brush. Soak,wash and rinse all with caution appropriate to acids.
This might make affordable sense if you plan to replace the chain in near future anyways.
Use a rust converter (changes ferrous oxide to markasite) to stop further rust if you want to say mount old chain on the wall like a trophy.