First be certain you aren't ascribing human behavior (anger) to your hen. Chickens aren't very likely to do stuff out of anger, at least it's not the same as human anger.
There is definitely a problem with aggression with some chickens, but it can have different causes, so you'd be faced with tailoring the solution to the cause. But first you need to figure out the cause.
To rule out dietary causes, if the hen isn't eating the feathers, this isn't likely the cause. If she is consuming the feathers, that sure makes things simple. But I've found feather picking is least likely to have a dietary cause, in spite of most people offering that as the cause when trying to help.
The nature of the feather picking offers a clue beyond whether the feathers are actually being eaten. Are you sure this is happening at night? Is there enough light for this hen to see to do it? Are the feathers being completely yanked out or are they being strafed, leaving them to look shredded and resembling fur, but otherwise still in place?
Is the skin being broken on the victims? Are there open wounds? If so, what are you doing for the victims to treat them?
Sometimes, when this behavior occurs, it's due to boredom. Other times it's because the perpetrator has a compulsion and is fixated on the feathers on certain areas of the bodies of its flock mates. It's in the brain.
I have a hen who has had this very aggravating behavior for six years. The behavior tapers off over winter, and in spring it flares up with a vengeance, indicating it may be seasonal and associated with hormones. She has both a compulsion and a boredom problem. She's helped by providing a flock block which helps to satisfy her destructive urges.
However, I can't really provide a cure for this. While I've never culled such a hen, having had a few over the years, I certainly have entertained the idea. It is, after all, the only real sure fire way to stop it.
