It could be just a sinus infection or at worst Mycoplasma. Separate the chick from the others. I think the best thing would be to get some Terramycin eye ointment. If the eye has any discharge, wipe it gently with a clean cotton ball before putting ointment in the eye. Some tetracycline...
I've seen Buff Leghorns from a guy named Dan Honour. Very good looking birds. I plan on getting back with Leghorns next year since it has been many years since I kept them. The California Greys I have lured me back.