3-speed drive trains should naturally have a straight chain line and lots of room for the chain, which is typically wider. I suspect the LBS did not correctly insert the chain pin, when reassembling. If this was the case the pin could be sticking out on one side and potentially catch on various drivetrain components. If the catch significant and the pin on one side is only partially inserted into the outer link body, eventually it will come apart and leave you stranded. Check where the chain broke to see if the pin at the break point is flush or sticking out 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!)

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!)