In a Christmas carol what does Marley's chain symbolize?

The chains that Marley wear symbolize all the mistakes that Marley made when he was alive. Built from the same mold as Scrooge, he was a miser and is warning Scrooge that if Scrooge doesn't change he will carry around these same chains but longer because Scrooge has lived longer than Marley. These chains are like the sins you have in your conscience. It is a burden.

Marley says "I wear the chain I forged in life. I made link by link, and yard by yard; I girded it on my own free will, and of my own free will I wore it. Is its pattern strange to you?"

Marley anguishes his mistakes and doesn't like the chains, he has learned to live with his mistakes and knows he can't change them.

To make a long story short, the chains symbolize mistakes and are a warning to Scrooge to change so he can escape the fate of Marley's.