i just got the tensioner in the mail TODAY to do this same thing for my wifes Jetta. and hers is doing the same death rattle after it warms up. had it towed 107 miles back home last week as i couldnt diagnose over the phone.
i have done this before, leave the chain i do/did.
takes about 30 minutes or so. do NOT pull the exhaust cam up, or you will be doing the timing belt stuff like possibly putting the belt tensioner back in to put a pin in it and retime the whole thing. i pull the intake cam up, mark a single tooth and one roller on the chain, and weasel the tensioner out of there. clean up and re-goop the new gasket you need, and then wiggle the tensioner back in. bolt down intake cam verifying that its still in the proper place, and close her up, doctor.