Yes, my chicken encyclopedia says that a few things besides lack of vitamin E can cause it.
ANYWHOO, back to the real topic of this thread.
I found another therad recently started by another BYCer who is having almost the exact same problem with one of her girls. Someone sugested eye worms...
If you can't wash it out then maybe she's got some sort of growth in her eye. I'm just guessing, but it very well could be. If it is she would need to have her eye removed if she was going to live. The eye is a straight path to the brain, so if she starts stargazing or she gets wry neck, then...
That looks like dirt or maybe (in your chicken's case) a dead louse or mite. If she's acting sick, well, I don't know a whole lot about disease which sucks. I need to do some reading
She could just be sleeping. Sometimes my girls act like "pirates" too. If this behavior continues, then do a closer examination. She might have a bug or piece of dirt in her eye. Post again if she doesn't start acting better soon.