I had a broody hen that killed two of her chicks but did not eat them. She raised her other six. There is a long story behind that. I've had a very few chicks die in the nest at hatch, I've never had another chicken eat one. I have not had a chicken eat the shells after the hen brought her chicks off the nest. I'm sure this kind of stuff can happen but I've never experienced it.
To me it is extremely unlikely that any chicken ate that without leaving a trace. Chickens can swallow a mouse so it's possible a chicken could eat a baby chick but before they eat that mouse they peck it until bones are broken and it is really limber. No way could they swallow a chick still in the shell. They'd have to soften it up first, just like the mouse.
If another chicken ate it they'd possibly carry it out to the run or somewhere. If they did that I'd expect to find bits of egg shell out there.
I've had a snake eat eggs out from under a broody hen during daylight. To me this is a strong possibility. The broody hen just sat there. The rest of the flock wasn't sounding an alarm, they often do if they see a large snake but they were outside so they didn't see it. It's possible something else got the egg without the flock or broody sounding an alarm but I really think snake. Maybe because that is what happened to me.
Have you cleaned out that nest and searched in the area to be very sure it is not there. I've had golf balls (fake eggs) disappear before and later find them in the bedding.
I don't have any more ideas as to what might have happened. From your threads I don't see that you are doing anything wrong to deserve this.
