You underestimate the murderous-ness of chickens.

Something a little like this:

Reminder that this is a stealth mission. You're gonna want a stealthier animal than a chicken. Imagine crawling through the dark in tense silence, only to to given away by a loud BKAWK. Not even a hobbit could sneak further than Moria with that condition.

Furthermore; The One Ring's greatest limitation is that it cannot just sprout legs and run off. Even beings of higher intelligence can be bent and manipulated to the ring's will (IE its ultimate goal of returning to Sauron). Putting the thing on an animal sounds like the best opportunity one could give an evil, tangentially sentient piece of jewelry the option to pilot the poor creature like a meat-mech directly into Sauron's clutches at the first opportunity.

As an aside: the ring could not be worn by said animal, it would needs be lashed to it. Imagine keeping track of a chicken which is now invisible to normal people, and also lit up like a beacon to the eye of Sauron and his otherwise day-blind ring wraiths. Bad idea.

how could it work?

whoever carries the chicken will be tempted by the ring and will likely kill the chicken in a fit of weakness

Someone has never owned chickens. They are capable of unspeakable acts

I have a hen that’s pretty bossy but for god sakes don’t give it to a rooster. A rooster would be king of Mordor in a hot second.

This sounds like a clip from a LOTR × Ghostbusters crossover. They try using a trap but the One Ring upgrades the trap to catch almost any spirit or demon, including Balrogs, tempting the Ghostbusters to use it to capture Sauron, which, of course, is pure folly.

They’d have eaten the chicken pretty fast.

Someone never played Zelda and it shows.

Do it Canadian style, with a Cobra Chicken.

There wouldn’t be anything else alive after that for sure.

One fowl to rule them all

It's been tried. Where do you think nazgǔl come from?

Well, first of all, the ring makes you invisible

Kite-Man: Hell Yeah. The Anti-Life Equation infects a chicken, and it proceeds to murder a lot of people.

It finds a way.

Why else did they have four hobbits in the fellowship?

You need a few spare mules in case you gotta put the first one down.

why dont they render the ring unusable by putting it on a larger metal ring

put the larger ring on gollum as a fancy bdsm slave collar and throw the whole happy and docile sub gollum off an eagle into mount doom

edit: how to put the ring over gollums head? idk weld it together once he wears it

Sam would make an excellent chicken sandwich with this Lembas bread.

Then the Chicken becomes an unwitting spy, and easy to steal from.