I get an occassional rat in spring & fall & have no problem getting rid of them. You get the green/yellow poison blocks. You pit it in the rat hole, cover it with a brick so chickens don't eat it and keep replacing block until you see it in there and no one's taken it. Voila! I just had to do it a couple of days ago. Only takes 2-3 blocks (if you're talking one rat) and they're dead cause I think they take it back to the nest. And I've never seen a dead rat out either for anyone to eat. Try it...it works!
I do the same thing for rats. I had one in my garage that could lick the peanut butter off a trap without springing it. I used the blocks. Done.
Then when we got the girls, one came through the back fence from my neighbor's nasty shed/deadfall pile. I put a few blocks out of reach of the chickens and now he's gone too.
If you can find it's pathway in, you should be able to set something up that the chickens can't get to.
Or Caleb could come down and shoot it!!