  We consider whether a discrepancy between the SLAC and LEP measurements of
$\Sw$ can be explained by new physics. We find that only the contribution of a
new neutral gauge boson, $Z^\prime$, nearly degenerate with the Z can affect
the SLAC measurement while leaving the LEP observables almost unaffected. We
briefly discuss possible signals for this new gauge boson, including changes in
the $Z$ lineshape when measured with polarised electrons, small changes in
$R_b$, $A^e_{FB}$, and larger changes in two jet and $t\bar{t}$ production at
hadron colliders.
