Well, they sure aren't new (factory originals on a 13-yo bike), but I have been able to tension the chain and cancel any noise until now...
Then again, I had the rear brake drum shoes swapped out a couple of months ago, and I noticed that the mechanic who worked on it made two asymmetrical marks on the adjusters, which however I evened out during my first attempt at retensioning, thinking that maybe it was a mistake on his part... or was it?