I was just about to make an almost identical post. I apparently have one hen who has begun consistently laying shelless eggs.
 
For a while I would find one here and there--on the chickenhouse floor, out in the yard--but it's settled into a regular, consistent pattern. Every morning I find a single shelless egg in the same place underneath the roosts on the poop board. 
 
I think I've got the guilty party identified, based on who I know is laying normal eggs and where everyone tends to roost. It's one of my Ameraucanas.
 
They're just over a year old. I feed them layer from Countryside Organics and they have free access to oyster shell and grit. They have a large yard with sand substrate that I keep scrupulously clean (seriously--I go out there and clean up poop several times a day. It's obsessive.) Most days I turn them out to forage in the back yard.
 
The rest of them are laying good, hard-shelled eggs, 5-6 per day from 7 hens.
 
No nighttime disturbances--we've got a neighborhood fox that comes around occasionally, but the coop and yard are more heavily secured than Quantico.
 
Any ideas? Is this possibly disease-related, and if so, is it treatable?