An analysis is performed of the three-particle Bose-Einstein (BE)
correlation function in the process
$e^{+}e^{-}\rightarrow  Z\rightarrow {hadrons}$ with the L3 detector at
LEP. The three-particle BE correlation function of like-charged pions and
the contribution to this function due to two-particle BE correlations are
measured. Genuine three-particle BE correlations are observed. In
particular, using a non-Gaussian (Edgeworth) parametrization we find
$\lambda=0.75\pm0.10\pm0.03$, measuring the strength of the correlations,
and $R=0.72\pm 0.08\pm 0.03$ fm, measuring the effective source size in
space-time. Combining this result with the measurement of two-particle BE
correlations, we find that the data are consistent with a fully incoherent
production mechanism of pions.