Your Subaru does indeed have a timing chain, and it does not normally need to be changed during the life of the vehicle.
Unlike timing belts, which have a finite life span and which require periodic replacement, timing chains typically last for at least 200,000 miles and many of them are still good at 300k. That factor, along with head gasket problems on some of their 4-cylinder engines, is one of the reasons why I chose a 6 cylinder Outback.
And, as andrew stated, if your timing chain is going to fail, you will hear it gving you a warning. If you hear what sounds like a chain beating or vibrating against a metal cover, that will be your warning sign. However, I don’t anticipate that you will ever hear this sound unless you fail to keep up with oil changes and/or allow the oil level to fall dangerously low. The modern Subaru six-cylinder engine is about as bullet-proof as it gets.