Submitted to Physical Review Letters

We present direct measurements of the neutral weak anomalous magnetic dipole moment, a w, and neutral weak electric dipole moment, d w, of the tau lepton. The dipole moments are measured by analyzing the decays of leptons produced in the annihilation of positrons and longitudinally polarized electrons on the Z boson resonance at the SLC. Using 6736 Z decays to + pairs selected from our 1993-1998 data sample we obtain Re(aw)=(0:26 1:24) 10 3