This is a common topic,

Summary

Q: When to change timing chain and sprockets?
A: BMW's offical line and the body of opinion on this forum is that it does not need done. It was never on the official service schedule.

Q: Do the chains break?
A: Duplex M3 chains don't break, but the sprockets can wear. There have been 1/2 stories of chains breaking, but no massive body of evidence that the break. There are forum cars where the work has not been done and the chains are still fine @ 130k+ miles.

Q: E36 M3 tensioner?
A: The E36 tensioner is not oil feed and therefore does not rely on oil pressure. In the majority of cases fitting one can stop the rattle on startup. It is a straight swap.
P/N 11 31 1 405 081

Q: Oil
A: what are the recommendations..?

Experiences

1: My car rattled badly for up to 10 minutes; hot or cold start.
I had the tensioner replaced and no difference was made.
It was replaced again just in case the new one was duff and the rattle remained.
So I had the chain done @76K miles. What a difference. Quiet startup and smoother engine. Cost £1000 using BMW parts fitted by an independant garage who have looked after loads of E30 M3s.
I inspected the chain and guides afterwards and they were very badly worn.

2: I had mine done by Hartlake BMW who did a great job for about £1300 with an E36 tensioner. I couldn't decide if it was worth doing but compared to a complete rebuild for a quoted £5500 (worst case if the chain broke) I thought it a worthwhile investment.

3: I have a 1990 E30 M3 with 100k on it and it ran as sweet as anything. It had no timing chain rattle at all even from stone cold. I fitted the E36 upgrade just as a safety precaution and it always runs on Mobil 1.
It went pop at Donington in 2003, the chain jumped a tooth or two when I was pulling 7700 rpm leaving the exhaust valves in the path of the fast approaching pistons,you can guess the rest. Not nice.
Bexley`s stripped it a couple of days later and the chain and sprockets where in very good condition with a bit of wear on the expensive bits but nothing excessive, what we did find was excessive end float in the crank.
So if you haven`t checked you end float lately wouldn`t be a bad idea, it could cost you your engine.

4: 210k+ miles and still on 1st chain with no problems.

Independant Garages 

Ajec Racing, Autobahn, Bexley's, Hartlake, http://www.moseleymotorsport.com/ - Moseley Motorsport , http://www.munichlegends.co.uk/ - Munich Legends , PCS, http://www.steverowleyvehicleservices.co.uk/ - Steve Rowley