Suitable remedy for chain damaged by bike shop
@Alexander is right, there is no need to break a chain when you replace a bottom bracket. So your hypothesis doesn't make complete sense, unless maybe they were doing other stuff to the bike?

So if you do take the bike back to the shop, odds are that that's their response.

I know if I got myself a new (second-hand) bike, I'd think about replacing the chain almost automatically. Same as something like brake pads. Just so you know where its come from, plus they're cheap enough its almost a no-brainer. 

By the looks of that cassette its an 8-speed, so you just need an 8-speed chain (e.g. http://www.kmcchain.eu/?en/products/multiple_speed/8_speed_derailleur/). Really common, any bike shop will have one. If you decide to buy off the web and fit it yourself (easy enough, just need a chain tool, which is an invaluable tool to have in any case), actually KMC is a decent brand to go for anyway.