Reconciling the LEP and SLAC measurements of sin$^{2}\vartheta_{w}$

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.