Also, check your local laws.
River otters are also protected from trapping, hunting, and other harvest in 17 states. However, 27 states have trapping seasons, and four states and two provinces have hunting seasons, accoding to Google's Generative AI - so I have no idea, really, how accurate...
I would not try to get rid of the otters, they are an important part of the ecosystem and were probsbly there long before you and your chickens. It's also entirely possible they are not your culprit; in that environment you're also likely to have raccoons, minks, foxes, coyotes, rats, skunks and...