Is it normal for the chain to slip in an 'extreme' gear? My bike's recently been in for a service so afterwards I checked that all the gears are shifting and working properly.

As part of my testing I put some power through the cranks in the photographed gear and found that the chain slipped. Having found that out, I tested it some more and it's very easy to get the chain to slip in that gear by putting some power through it.

Is that normal? Could it be the derailleur set up at fault?

I don't ever use this gear day-to-day so it doesn't really matter I suppose. However, I'd like to think that everything was 100% working okay having paid for a service.

Should a service leave a bike in this kind of state? The bike's 11 months old and hasn't been heavily used in that time.
In that extreme cross chain configuration you have the maximum amount of chain for the derailleur to take up.  And you also have the least amount of chain tension.  Combine that with on the least number of teeth engaged and you have the configuration that is most likely to jump.  

Should it jump no.  

It is a shop problem - maybe.  

In just 11 months the spring in the derailleur could have weakened.

Or if you ride on the small gear in the rear even a bit it will wear and new chain might skip.  But given it does not skip on other front gears I would chalk it up to chain tension.

The shop may have too many chain lengths.  In biggest front and rear could a chain length be removed? 

Cross chaining a road bike or the first two chain rings is something that happens.  But on a mountain bike in the granny gear that extreme cross chaining is just not something that should come up.  I would not put that kind of stress on a chain even to test.

Some front derailleur have a trim for big to big.  This make sense to me as you may come to a stop but will get back up to speed soon.  And now you have maximum teeth evolved.  I don't know if trims comes in a 3 speed and it would make less sense as the outer is out further.  Even with a trim cross chaining puts more stress on the chain and other components and is not as efficient.

The question is not about specifically about cross chaining but here is a link.
Technical Details and Implications of Cross Chaining

Not the question but the smaller rear gears are going to wear the fastest as they share the load across fewer teeth.  So go for a larger front ring when you have choice. But still avoid cross chaining (a lot).