What is causing rumble in drive-train (not engine or trans), that goes away when turning to left.

Rumble is at all speeds above 25 mph. Is present at speed even when automatic trans is placed in neutral and engine sped drops to idle. Rumble goes away when making left hand turn, but right turn does not effect rumble. Examination of tires does not evidence any cupping or unusual wear pattern.

I agree with the others -- get it on a lift and check the wheel bearings. VERIFY which side , or plan on doing both!

Folks - it was the left rear wheel bearing that was failing...in concert with a sticking parking brake (which I never use) and sticking left/right rear brake calipers. Perhaps not surprising for a 9 yr old car with 165k miles. Most disappointing was that this all was missed during my recent oil change visit to the Toyota dealer, and my complaint about the rumbling sound, and the technician's test drive. Took it to Sears on Thursday and they figured it out right away. Thanks for all the good advice.