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 fb(-1) of data collected at an e+e- center-of-mass energy of 10.58 GeV with the BABAR detector at the SLAC 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 B(tau-->lhh')<(0.7 - 4.8) x 10(-7) at 90% confidence level.