The toilet flapper chain broke, and someone flushed the toilet, and the chain (apparently) got sucked out of the tank into the bowl. It appears to be caught in the small hole that's in the front of the bowl. I jiggled the chain with a pliers, but I'm not sure if there's anything I can do to try and get it free.
The chain is lightweight and is floating a bit. I presume the clip is what's causing it to get trapped.
I found a couple of diagrams that look a little like my toilet:
Here, where it says "jet": http://www.upfrontprice.com/images/Clipart/flush%20action%201.gif
And here's a larger diagram, showing how water flows, which I presume is how the chain got pulled into it: https://s3.
