Q: Timing chain tensioner rattling on a 2003 Audi A4

Yes it does, but it should never rattle of course. The problem with yours is that the timing chain probably needs to be replaced because it has too much slack there or in the tensioner. Changing the timing chain is very expensive job on an Audi, but changing the tensioner isn’t that bad of a job. So I would advise you to get a new timing chain tensioner put on. And probably, if you don’t change your oil that often, and your oil gets black--change the oil more often, because those tensioners have tiny little holes that the oil has to come through. If it gets dirty and it clogs up, that is exactly what happens and it won’t work right away and it takes time to build up pressure.