  A search for lepton-flavor and lepton-number violation in the decay of the
tau lepton into one charged lepton and two charged hadrons is performed using
221.4 $\mathrm{fb}^{-1}$ of data collected at an $e^+e^-$ center-of-mass energy
of 10.58 GeV with the BaBar detector at the PEP-II storage ring. In all 14
decay modes considered, the observed data are compatible with background
expectations, and upper limits are set in the range ${\cal B}(\tau\to\ell
hh')<(0.7-4.8)\times 10^{-7}$ at 90% confidence level.
