It means that the only thing you can lose (if you do this) is your chains. You won't lose your pride, your health, your education, your friends, etc.
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The word 'chains' is normally used figuratively in this context. It refers to all the things that reduce your freedom.
The phrase is derived from a famous quote by Karl Marx.
"Workers of the world, unite! ... You have nothing to lose but your chains!" Here, 'chains' refers primarily to the way in which the social structure of society and its associated economic s