We have analyzed one-prong τ decays with neutral kaons using the information from a fine-grained hadron calorimeter. The data sample consists of 43 500 Z → τ+τ−(γ) events collected by the L3 detector at LEP in 1991, 1992 and 1993. The following branching fractions are measured:
B(τ− → ν-π Kº) = 0.0095 ± 0.0015 (stat) ± 0.0006(syst);
B(τ− → vπºKº) = 0.0041 ± 0.0012(stat) ± 0.0003(syst) and
B(τ− → vπ-K°Kº) = 0.0031 ± 0.0012(stat) ± 0.0004( syst).