  Bose-Einstein Correlations (BEC) of three identical charged pions were
studied in 4 x 10^6 hadronic Z^0 decays recorded with the OPAL detector at LEP.
The genuine three-pion correlations, corrected for the Coulomb effect, were
separated from the known two-pion correlations by a new subtraction procedure.
A significant genuine three-pion BEC enhancement near threshold was observed
having an emitter source radius of r_3 = 0.580 +/- 0.004 (stat.) +/- 0.029
(syst.) fm and a strength of \lambda_3 = 0.504 +/- 0.010 (stat.) +/- 0.041
(syst.). The Coulomb correction was found to increase the \lambda_3 value by
\~9% and to reduce r_3 by ~6%. The measured \lambda_3 corresponds to a value of
0.707 +/- 0.014 (stat.) +/- 0.078 (syst.) when one takes into account the
three-pion sample purity. A relation between the two-pion and the three-pion
source parameters is discussed.
