Is it her nictitating membrane--the inner, third lid that closes vertically that she's closing? There IS a parasite that can cause problems with it, but it is found mostly in sub-tropical regions:

http://www.merckvetmanual.com/mvm/index.jsp?cfile=htm/bc/202800.htm

Scroll down to 'O Mansoni' and see if it fits. Be careful with the antibiotic ointment, most of them say very specifically that they are not for opthalmic use. If she has an ongoing eye or head infection (sinus) or Infectious Coryza, you may have better luck with oral antibiotics or a medication such as Sulmet. Any foamy discharge from her eyes or other symptoms, such as weight loss or abnormal poops? 3 1/2 months is a long time. :(

Velvet ~:>

It's the lid that closes up from the bottom of her eyes. I really don't think it's an infection. The lid (usually the left one) just seems stuck. The next time I have chance I will look for the o mansoni though I would worry that I might damage her eye in the process. We are in northern Wisconsin so I would be surprised if that were the problem. I will not use any more Neosporin--I just put it around her eye which probably didn't do any harm or good.
I hesitate to give her Sulmet. Other than the eye(s) she is very healthy. She's the only one small enough to fit under the garden gate so she spends a lot of time in the garden helping herself. She has a small waterer and food there and I always give her treats. While she is small, she is not at all thin. She still sleeps with 4 of her clutch-mates, 2 of them bantams. I will continue to keep a close eye on her. Her name is Reise, short for Tyresias, the blind seer in Oedipus.
Thank you, Velvet. All my chickens thank you, too!