https://www.amazon.com/dp/B0DQ89XXC8?ref_=ppx_hzsearch_conn_dt_b_fed_asin_title_1
I recently bought this product. All-natural, made from a combination of essential oils like peppermint & lemongrass, relatively inexpensive, humane. Clean & hygienic in little self-contained pouches (although you don't want to ingest any of this stuff!) I've used it for only a week in our attic, where rats pop up every few weeks. So far, no rats whatsoever, although it's definitely too soon to make any conclusions about whether this product is effective. But IMHO it's definitely worth a try before resorting to more extreme methods.
Re: the wide range of opinions here about peppermint oil deterring rodents, well, it appears that sometimes it works, sometimes it doesn't, sometimes it takes a while to start or stop working. Details matter.
Here's what Microsoft's Windows AI has to say on the topic (including links):
"Yes, peppermint oil can help repel rodents due to its strong scent, which irritates their sensitive olfactory systems2. However, it is not a foolproof solution and works best as part of a broader pest control strategy"
https://www.thespruce.com/peppermint-oil-for-mice-7373740
https://pestpointers.com/how-to-make-an-easy-mice-repellent-using-peppermint-oil/?form=MG0AV3
Hope this helps. I share your worldview about killing pests only as a last resort. However, I also want to stress that chickens do need to get outside once in a while, maybe at least once a day. They're not designed for life indoors. One of our birds was a rescue chick, almost killed by two protective hens. We raised her indoors and even though she's now adult, she still will only go outside when we're with her. But we still take her out for at least an hour a day, while we're outside, and have been slowly, slowly convincing her not to be afraid of the other birds. She was so badly traumatized as a week-old baby that she may never fully acclimate to "normal" chicken society, but we're hopeful that someday she'll be ready to do so.
Sorry to digress. I still recommend at least trying the pouches at the Amazon link, as a convenient, clean, and potentially effective way to solve your problem. You might also want to invest in an automatic chicken feeder that keeps food locked up until opened by an adult bird. I think that might help A LOT.