When you hear of chain failure in the S4 motor it is in fact the cam adjusters, chain tensioners, and chain guides that wear out / break. There have been no issues to our knowledge of an actual chain snapping.
you need to replace the timing belt eventually, But that is completely different. the timing chain is a full engine removal. as long as you keep the right oil in the engine and perform regular oil changes, you shouldn't have to worry about the timing chain. i have a '10 S4 with 125k miles and it runs great.
Timing chain: Audi A4 2.0 TFSI quattro 2013 – 2016: 211 hp: Timing chain: Audi A4 2.0 TFSI quattro 2013 – 2016: 225 hp: Timing chain: Audi S4 2013 – 2016: 333 hp: Timing chain: Audi RS 4 2013 – 2016: 450 hp: Timing chain: Audi A4 2.0 TDI 2013 – 2016: 136 hp: 210 000 kilometres: Audi A4 2.0 TDI DPF 2013 – 2016: 143 hp: 210 000
Bumper cover and front clip is only an hour or so, so dropping the engine to get to the rear chains is a curious call. And bunch of other parts. Search for Audi A8 4.2 BVJ timing chain replacement Forum Some info on the cooler/O-rings replacement and other parts to replace while the front clip is off in discussion here within DasuberS8's thread.