Trying to translate a song lyric that says, "I will break off every binding chain." Really no idea what to do with that. The best thing I could think to come up with would be something along the lines of, "cxircauxfermigema cxeno"
But I feel like that's a lot of cumbersome morphemes, and don't really know if that even accurately represents what I'm trying to say.

I looked up "binding" and "to bind" in several dictionaries, the only translations they give me are in the sense that something would be legally binding.

Any alternative?

Mi rompos ĉiujn katenantajn ĉenojn.

More suggestions:

Mi frakasos ĉiun ĉeneron.
Mi fortranĉos ĉiun ŝnuron.

For lyrics you can take advantage of the context to keep things short and simple, even if not every shade of meaning is preserved.

Mi frakasos chiun katenajhon

You don't need a literal translation, probably, in this case.

"To bind" would be ligi.

Okay, thanks for the help. Just out of curiosity, would "cxirkauxfermigeman" or "cxirkauxfermantan" even be anywhere close to what I was trying to say?

The first one, cxirkauxfermigema, means "inclined to cause something to close [something] around [something]". The second means "closing something around [something]"

fermi = to close, transitive. That is, you would use "fermi" for "I closed the cabinet", but if you wanted to say "the door closed behind me", it would be "la pordo fermigxis malantaux mi" (lit. became closed without specifying who did it).

fermigi = to cause someone or something to close [something]. Adding -ig- to a transitive verb makes the meaning "to cause someone to do [something transitive]".

English makes this verb confusing. It is clear to us in English that "eat" is transitive only (you can eat an apple but the apple doesn't eat - you have to say it *is eaten*). But "close" is both transitive and intransitive, you can close a cabinet, and say that the cabinet closes, we are not forced to say "the cabinet is closed". Fermi is transitive only. There are a number of these verbs in Esperanto, whose transitivity is a little hard to remember because their English translation acts both transitively and intransitively. To mix, to break, to burn - these are some other examples.

Getting back to your question, I would not say that closing something around something is the precise equivalent of binding, "ligi" would really be better. But it does have the idea perhaps of imprisoning or backing someone into a corner. It would have to be "cxirkauxfermigxanta", something being closed around something. cxirkauxfermigxema would be something inclined to be closed around something, -em- is not used as frequently for inanimate objects as for animate objects. I could certainly say a broken door is malfermigxema (inclined to open up, won't stay closed), but if it's a thing that is in good repair and functions to open or close on command, I'd hesitate to use "fermigxema" or "malfermigxema" on it.

According to the PIV, a kateno is a ĉeno meant to bind someone.

katen/o
1 Fortika ĉeno, uzata por ligi la malliberulojn k malhelpi ilin forkuri: oni enpremis liajn piedojn en katenojn; la malbona homo en la katenoj; pundoma kateno; memoru miajn katenojn. ☞ ĉeno, ŝnuro, ligilo.

I would go with "Mi (de)rompos ĉiun katenon."