How do you know for certain that the alternator is OK?

I may be incorrect but the alternator may have replaceable diodes. But,
on the other hand, it's 30 years old and its brushes may have worn out.
These too may be replaceable items.

Timing chains cannot be heard at high rpms. Forget that.

Timing chains wear and stretch. The chain should be replaced when the
camshaft is 5 degrees or more behind the crankshaft. This is found by
removing the valve cover and s/b done during a valve adjustment (needed
every 15K miles).

There's a notched collar immediately behind the chain sprocket. Rotate
the engine (in the correct direction) by the crankshaft (pull on the
drive belts) until the notch is aligned with a groove cut into the
driver's side of the front camshaft support. The cam is then at its TDC
or 00 degrees position. Then read the crankshaft's angle down at the
harmonic balancer and main pulleys. That's the governing reading for the
chain's replacement; it s/b =< 5 degrees ahead of the cam.

The valves ought to be adjusted every 15K miles. If not done the engine
loses some power, and becomes hard to start due to lost compression,
especially in cold weather. You can do this adjustment, it's not difficult.

Otherwise, this is a very simple engine to maintain. Change the oil and
filter every 5K miles, fuel filters 15K miles and air filter at 30K. The
fabric covered bleed off hoses between injectors get heat fatigue, begin
to leak and need to be replaced after a few years. That's another simple
DIY job. Don't hesitate about any of this for the motor is designed for
DIY owners.

Good luck with it.

Ok so what's between the alternator and the battery? Wires? They
aint working. Get a voltmeter and find out where the electrons
stop.

Also, on any MB of that era  and without looking it at I can
tell you the grounds are fragged and that could be it too. Take
them off, clean them to within an inch of their lives then a bit
more, clean up where they attach then put them back with some
dielectric grease slathered on the outside. Or vasoline.

Nah, it's easy, you can do it yourself. Ask here if you get stuck,
operators are standing by.

You already know. If the previous owner says it needs a chain IT NEEDS
A CHAIN. Whenhte fail the engine is a heap of smoking rubble, It's the
one thing you don't mess around with.

It's 3-4 hours labour at worst, an an hour at best. Chain is about
$75-$100.