My chain came out of dérailleur frame, but gap seems too small, am I misunderstanding something? So the chain came off my bike on the way to work this morning, but when I tried to put it back on, it seems like it has also come out of the dérailleur frame, but the gap where it seems to have come through is much too small for it to fit back through.



The red arrow shows where there is a kind of metal peg, sticking out from the 

There's a gap then, between this metal peg, and the other side of the dérailleur mechanism frame, shown by the blue arrow.

It doesn't seem possible for the chain to fit through this gap, because the gap is too small.

I opened and closed the chain before, so I guess I can do this again, to get it back inside the dérailleur mechanism frame, but what's bothering me is:

Since the chain doesn't fit through the gap, how did it get out through this gap in the first place.
And then, does this apparent impossibility to fit through the gap mean that I'm misunderstanding something about how this is supposed to work? 

And the practical question is then: what exactly do I need to do in this situation to fix this problem (as easily as possible).

The chain is not broken.
To fix it, you don't have to break the chain. Simply unscrew one or both of the derailer pulleys slightly until you have enough space to get the chain through.