*railer's chain
I'm hearing “railing chain” (or railin') which is the expression I remember from practical usage:
Ashley & Foster Bay Rum Blues (1933)

A hitching rail made of chain. Clothes rail is the same usage. A “rail line” or “rail string” is what makes for a “string of horses.” Just no retrievable sources for any of it. Darn!

I did manage to locate a sledge gang video in the hunt (freemen, so no railing chain though.) Post it later.