According to Frank Barrett's Illustrated Buyer's Guide to Mercedes Benz, 1981-1983 380 engines had the single row timing chain. Beginning in 1984 MB began using the double row timing chain.
With the single row chain, (which by the way was unique to the U.S. - in Europe they always had a double row timing chain) if the oil wasn't changed frequently, friction under load would cause the chain to wear and stretch. If a single row chain jumped a tooth on its sprockets, the valves would hit the pistons, with expensive consequences.
Still, even with the doulbe row timing chain, the chains do stretch on these M116 and M117 engines over time, because the chains are long and change direction many times as they travel from the crank at the bottom up to each cam on each side of the "V".
Most members and techs on this site recommend replacing the chains approximately every 100,000 - 120,000 miles. 4 degrees of stretch is considered the time to change the chain.
Further, it's not just the chain that's the problem. The chain guide rails are made of plastic, and become hard and brittle over time, as well. As the chain stretches it becomes loose, and starts to rattle and bang and slap against the guides. It usually happens at start-up, but when the chain gets loose enough and the guide rails are old and brittle enough, the chain will slap against the plastic and it'll break apart. Plastic pieces will get stuck in the chain and the sprocket, and bam!, you've bend a camshaft, pistons will hit valves, etc.
I've found from reading posts on this site, that's it's more often a loose chain breaking old guide rails, than a loose chain jumping a sprocket that causes an engine failure.
Either way, your car is due for a timing chain replacement and upper guide rails. You asked about a chain adjustment, but there is none.
Just like Nike says, Do it. Do it now.
2001 E430, Bourdeaux Red, Oyster interior.
1973 280SE 4.5, 170,000 miles. 568 Signal Red, Black MB Tex. "The Red Baron".