sounds like you've got a greyling spawn (or something else) inside your base or something, right on top of your chicken coup.
might wanna make a workbench that covers their whole exhibit to prevent that.

my chickens don't die. i get plenty of eggs, i have no trouble hatching eggs.

if you absolutely cannot fix it, put a wolf sentry near the coup or even inside of it. he will kill whatever enemies spawn in there.

that is assuming you actually went out of your way to tame a wolf.