Chains usually only break when lateral force is applied to them. To have one break on a single speed drivetrain is fairly rare. I'm gunna give your LBS the benefit of a doubt and assume they installed the chain correctly. The problem with changing just your chain is that it's only one piece of a system that wears as a unit. As your chain wears it actually gets longer, this is a result of the friction from the pins taking metal off of the inside of the bushing in each link, which lengthens the measurable distance between each pin.
As a result, the cog starts to wear on the pull side of each tooth.
An example of an excessively worn cog:
When you put a new chain on a worn cog they won't necessarily mesh. The new chain will have some "wiggle room" to slide around in and possibly even slide laterally enough that one of the sharpened teeth can pick up a link, which on a single speed can put enough force on the one side of the link to pop the pin out.
My question for you would be, how worn was the cog? If the cog is fine, then how loose was your chain? A loose chain can just as easily jump the teeth and break.