  A search for the lepton flavour violating decays $\tau^- \to l^-
K^0_{\scriptscriptstyle S}$ ($l = e$ or $\mu$) has been performed using a data
sample corresponding to an integrated luminosity of 469 ${fb}^{-1}$, collected
with the {\slshape B\kern-0.1em{\smaller A}\kern-0.1em B\kern-0.1em{\smaller
A\kern-0.2em R}} detector at the SLAC PEP-II $e^+e^-$ asymmetric energy
collider. No statistically significant signal has been observed in either
channel and the estimated upper limits on branching fractions are ${\cal
B}(\tau^- \to e^- K^0_{\scriptscriptstyle S}) < 3.3 \times 10^{-8}$ and ${\cal
B}(\tau^- \to \mu^- K^0_{\scriptscriptstyle S}) < 4.0 \times 10^{-8}$ at 90%
confidence level.
