Funny

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.