Is there a timing belt in my Prius?

No, it has a timing chain.

 

Timing chains have a long life and make sufficient noise before failing to warn you to maintain them.

JeffD

 

In Prius it will probably outlive engine itself. And engine if well maintained will probably outlive the car. Low oil level will shorten both the chain and engine life. So check our oil.


In some cars you typically have replace chain at least once in lifetime of the car.

 

While there is no timing belt, the water pump is belt driven.

 

^ True, but it is externally mounted and in today's modern engine compartment it's relatively easy to change. Unlike a chain driven water pump in a 4th gen Maxima which is a chore to change. To the OP, the Pri water pump also has an early warning mechanism built into it to monitor its condition in the form of a weep hole. If you see pink/light pink crusty stuff around your water pump or what looks to be line of discoloration on the passenger side under your hood amongst other things its time to replace the water pump.