I also should add that when I found Lemon she was not in the nesting box, but the box had some blood and an egg that looked like a deflated balloon.
I'm so sorry for your loss. This is also my first year with chickens, so I have not experienced this personally, but as the other two posters said, it sounds like a prolapse. I was reading this article and it says that if the other chickens start pecking at the prolapsed vent, it will pull the intestines out and the hen will die. So if she was in the coop with the others maybe that's what happened. Again, I'm so sorry. Here's the link to the article:
http://www.the-chicken-chick.com/2012/04/prolapse-vent-causes-treatment-graphic.html?m=1