We have searched for a CP violation signature arising from an electric dipole moment (dτ) of the τ lepton in the e+e- → τ+τ- reaction. Using an optimal observable method and 29.5 fb-1 of data collected with the Belle detector at the KEKB collider at √s= 10.58 GeV, we find Re(dτ) = (1.15 ± 1.70) × 10-17 ecm and Im(dτ) = (-0.83 ± 0.86) × 10-17 ecm and set the 95% confidence level limits -2.2 x 10-17 < Re(dτ) < 4.5 × 10-17 ecm and -2.5 x 10-17 < Im(dτ) < 0.8 x 10-17 ecm. © 2002 Elsevier Science B.V. All rights reserved.