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