Sliding chain back on hub gear bikes
I also have a folding bike with a 3-speed hub (Shimano Nexus 3). My bike has a chain protection cover in the front chainring, so I find it harder to follow those other suggestions. I usually prefer to put the chain over the front sprocket in the first place.

The chain is also as tight as I can, but sometimes it happens that it falls over. I have noticed this happens when pedaling on a more irregular road or over bumps, so I just stop pedaling for a moment or go slower.

This trick is pretty easy and fast:


Grab the chain and put it over the rear sprocket (assuming it is already over the top of the front sprocket).
Because the chain is tight, probably, it will only be possible to move it over one or two teeth -- no problem.
Let the bike go backwards a little bit. The rear sprocket will spin together with the wheel and it will pull the chain over the sprocket.