New chain snaps after shop service

Chances are they misaligned the gears a little. I've snapped a few new chains and the most common circumstance is after I've messed with my gear indexing (I'd say "sorting out" but breaking a chain indicates it didn't work). There IS a chance that it's just a bad chain but it's also possible you did something wrong too.

I'd call the bike shop and tell them and see what they say rather than accusing them. If you bought the chain online, call the online retailer and speak to them too.

The work they did doesn't require the chain to be removed (as others have mentioned). It could be a defect but once again, the prices of chain are way to cheap to worry about it. Given the volume of chain SRAM puts out, one in a million chance. The rest of the chain is fine however so remove the broken link and keep on riding.

When adding links, chain pins can be tricky to get right. It requires a close eye and very small adjustments to make sure the pin is in correctly. Take note that when using chain tools, it will squish the link parts tightly together so that they do not move. You have to then apply force in the opposite direction to make them move freely. I learned all this from a Bicycle Tutor video (now pay-walled last time I checked), but I'm sure Youtube has more.

The first time I had to replace a chain, I made it too short at first, but then added some to it. It worked great for a week until it popped just as I was leaving for work (well a mile down the road). It failed at the spot that I had to add the links at. I pushed the pin in too far and didn't give the plate enough pin to bite into.

I have done a few more chains since then and found that I have to go slow and make fine adjustments (1/8 of a turn). Compare with the links around it to make sure it looks right, that the gaps are spaced right, and then only apply just as much force needed to make it move freely.