When do you need to change a timing chain on an 2001 Saturn 2001?

If it is a mechanical chain, then NEVER!!! It is part of the Engine.

If it is a SOFT CAM BELT, then at the recommended mileages; usually about 30,000 - 50,000 miles, depending on engine and manufacturer.

If a soft cam belt snaps/breaks, then it will wreck the engine. So if you are in any doubt about its last change, then change the soft cam belt, and note the mileage(s).