Does the 2008 BMW 528i have a timing belt or chain?

The 2008 BMW 528i uses a timing chain, which typically doesn't need replacing, and only needs proper maintenance in the form of lubrication to offer a long life. That said, what will need replacing typically will be the tensioner, water pump, and other parts that facilitate the chain's functionality. A new timing chain tensioner, for the genuine BMW part, is going to run about $90 and labor will typically be around $50. Note, if the tensioner has failed, it could actually damage the chain itself, as well as polluting the oil with foreign debris, so while a chain is really mostly maintenance free, do keep up on visual inspections of the rest of the system.