On my Wife's car (99 Alero, 3.4, all options) all the usual warning lights come on (ABS, Low Trac etc.) at random times, but what really drives her nuts is the warning chime. Is there a way to disconnect/turn off the audible alarm??

Thanks in advance.....

Low brake fluid, or a bad wheel hub, or corroded/broken wheel speed sensor wires are common causes of Trac/ABS/Brake lights on these cars. All but the hub can be diagnosed and fixed in your driveway, and sometimes it's possible to diagnose a hub without a GM scanner also.
Back to your question-No, the warning chime works through the factory radio, so the only way to disable it is to install an aftermarket radio.