Where are you located? The eye looks very infected, and there is pus around the eyeball that needs to come out. It could be from a peck injury, from getting something stuck in the eye that has caused an abscess, or it could be a sign of a respiratory sinus infection. A vet would be helpful. I would try to clean the eye with saline, QTips, and get the pus out. If you can get antibiotic drops or ointment, apply some twice a day after cleaning the eye. Terramycin, Neosporin, Ciprofloxacin are all good ones. Here are some graphic videos on getting pus out of the eye:
I contacted the academic veterinarian clinic and they recommended antibiotics suplha based drugs. They suspect coryza. But since it is only one hen, it might be either way.
I took her to the local vet, and they opened the eye and cut out the abscess. This vet that cut out the abscess doesn't think it is coryza, but an infections caused by something like a peck in the eye.
She gave eyedrops, and a solvent antibiotic solution. As well as pain medication.
Good that you could see a vet and get the eye abscess tended to. Did her eye or face have a bad odor before it was cut open? Eye peck injuries, and foreign bodies cannget into the eye causing an abscess. Those do look similar to pus that develops in eyes feom sinus and respiratory infections. Please let us know how she gets along.