I have a JRT. She was a stray along the road who almost got killed by a truck, so she came to me at 3yo. She's an excellent dog for predators. She's killed racoons that are twice her size. She's also came in at 1am with a six inch slash clear through the skin. I've had to reach up to my shoulder to pull her out of a ground hog hole because she had one trapped down there. She's cleared the farm of ground hogs, racoons, mice, rabbits, turkeys (scares them off).
She doesn't bother the chickens, but it is ONLY because I got chicks and started them indoors. Anytime that she'd go at them, she was flipped on her back and I gave a STRONG, LOUD, and in no uncertain terms "come to Jesus" discussion. So, she doesn't bother them, but I can clearly see that she has to work to fight her instinct because they are the same size as her normal prey. She's also run off all the feral cats, but leaves the two farm cats alone *for the most part*.
If you want something that will terrorize predators relentlessly (if not out right kill them), a JRT is a brave and bold dog that will get the job done and have a ball doing it.
If you want something to "protect" your chickens, that is not a JRT. Mine doesn't bother them, but she also doesn't have a protective instinct. If another dog came at the chickens, I'm certain that her instict would overcome her desire to be a good dog and she'd join in the chase.
I lost all my birds last fall and am working on improving my hen house and pen (I lost them to a weasel)... While I wish my birds could just free range all day, I will likely let them out around noon and only let them have half days when I get new ones.
I have horses, so while I love many herding dog breeds, I won't get one for the farm because I'm convinced that they would spend the day herding the chickens.