We have analyzed one-prong tau decays with neutral kaons using the inf
ormation from a fine-grained hadron calorimeter. The data sample consi
sts of 43 500 Z --> tau(+) tau(-) (gamma) events collected by the L3 d
etector at LEP in 1991, 1992 and 1993. The following branching fractio
ns are measured: Beta(tau(-) --> upsilon(tau)pi(-)($) over bar K-0) =
0.0095 +/- 0.0015(stat) +/- 0.0006(syst); Beta(tau(-) --> nu(tau)pi(-)
pi(0) ($) over bar K-0) = 0.0041 +/- 0.0012(stat) +/- 0.0003(syst) and
Beta(tau(-) -->nu(tau)pi(-)($) over bar K-0 ($) over bar K-0) = 0.003
1 +/- 0.0012(stat) +/- 0.0004( syst).