Good evening fellow enthusiasts!
I just picked up a wonderful 2013 XJL Supercharged and am getting ready for some Spring/Summer jaunts in the southwest of the USA. The only issue troubling me is the sound the engine makes after a cold start, a sort of rattle that is intermittent on the best of days. I am not sure if something is loose or if this is the telltale audible warning of a timing chain issue. Before I head to the local Jaguar Service Center I'd like to get an opinion from those that may have had experienced this issue or at least recognize the sound as a potential issue. Apologies if the sound in the video is a bit off, but the intermittent pattern takes shape closer to the end of the video.


Any thoughts are appreciated! Thank you!

 

It sounds a lot like the infamous worn SC coupler/torsion isolator rattle to me.
Plenty about this noise on this forum and elsewhere, just search for "supercharger coupler rattle".
The big give away that this is the cause of the noise is a loud "clonk" on engine shut down, from the top of the engine.
You may not hear the clonk on every shut down, in my case it was around every third time.
It's more an annoyance than a big problem but if let go for too long (50,000 miles plus) it can result in a badly chewed up SC drive shaft and eventually destroy the SC bearings.
Can be a relatively simple fix (just replace the coupler) but expensive as lots of labour involved due to having to remove the SC first.
All that said it could be something else such as a worn SC belt tensioner, worn/loose timing chain(s), worn high pressure fuel pump etc etc but my money is on the SC coupler.

 

If you plan to rely on a dealer for service I hope you have saved up your money.
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Try removing the supercharger belt temporarily to see if it still makes the noise.