It's called a "lash egg" and is the sad sign of internal infection (salpingitis) in the egg duct.
It is actually hardened puss.
It is important to track down which hen is doing this. She will need to see a vet and a round of antibiotics in hopes of quelling the internal infection, but it might be cancer as well. So, even with care, the prognosis is poor. Most hens die within a few months of laying a lash egg.
Thank you. Dang. I looked online and other people's examples of lash eggs definitely look more "plump" but I have no reason to disagree. No idea which of the girls it is yet though. Might not find out until she's dead....