Is this "chorus effect" more pronounced when you play an open A string? And do you have a continuous buzz sound?
Failing power supply filter caps can cause this. You get excessive AC ripple, which causes the buzz, and the power supply actually resonates somewhat (especially on the open A), causing the weird sound. If the amp's old, it's due for new caps. Sometimes (but not always) the filter caps can bulge or vent out electrolyte as they age, if you see any kind of white crusty stuff on the ends or bulging they must be replaced.
A microphonic tube can also make weird things happen too.