What could cause the bicycle chain to break? I'm on an old Muji 3-speed commuter bicycle which uses an internal Shimano gear hub, and I recently (3 months ago) got my bike chain changed by my LBS. 

For about 2 weeks I felt the chain would "catch", the way it feels when you're trying to change gears on a bike with derailleurs, and last night on my way home, the chain broke. Is this because the chain didn't fit well?
3-speed drive trains should naturally have a straight chain line and lots of room for the chain, which is typically wider. So I doubt that the chain is too wide.

I suspect the LBS did not correctly insert the chain pin, when reassembling.   If this was the case the pin could be protrude on one side and potentially catch on various drivetrain components.  Continually catching will stress the chain. If the protrusion is significant enough to catch, on the opposite side of the protrusion the pin may not be sufficiently inserted into the outer link plate. Eventually the catching could cause the partially inserted pin to pop out of place, breaking the chain, leaving you stranded. Check where the chain broke to see if the pin at the break point is reasonably flush to the outer link plate or protruding by a large amount on the side where the pin is still in place.

Speculation Warning

This is of course rampant speculation, as I have no pictures to go off of, but is the only logical mechanism that comes to mind.  (And it is something I have actually done and can verify can happen!)