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The fishers around my yard say yummy and frequent the pond and the brook that runs through my property. We have several kinds of ducks and other fisher bait that frequent that area.
I had to look them up I have never heard of one before.
From a quick search it seems like they will eat anything about there size or smaller. I would safely assume that if they could get into your coop with your chickens then they probably would eat one. They basicaly like anything they can get to eat, they are not to picky.
Fishers and martins are both chicken-killers. Coop and run security is the most important thing here. Trapping and disposing is secondary. Tunnel-proofing run, and hot wire for both run and coop if separate is good start.