Do you mean a squealing, feedback-like noise, or just a constant tone that never goes away and never changes?
If it's the latter, it could simply be picking up interference. A high-frequency lighting dimmer in the shop could create this sort of noise, or it could even be caused by the emissions of a nearby mobile phone mast.
I've got a similar problem. When I'm practicing at home, my 4003's single-coils pick up a weird high-pitched sound, like someone playing a bad chord on the highest notes of a Hammond organ with vibrato! I have never yet been able to pin down where it's coming from.
