Does the 2008 Audi A6 have a timing belt or chain?

This 2008 AudiA6 makes use of a timing chain, not a belt. A timing chain is designed to last the entire operational life span of the vehicle, so assuming all goes well then You should not need to bother with it. That said it can still be damaged and in some cases fail. If this happens You will notice that the car will almost immediately overheat. If You need to replace it then it will cost You about 100 dollars for the new part, and another 100 for the labor. Be cautious when buying a chain online. Some retailers will refer to both a timing chain and a timing belt as a cam belt. A timing belt will not work, and You may end up stuck with a useless part.