A search for the lightest neutral CP-even and neutral CP-odd Higgs bosons of the minimal supersymmetric standard model is performed using 216.6 pb−1 of data collected with the L3 detector at LEP at centre-of-mass energies between 203 and 209 GeV. No indication of a signal is found. Including our results from lower centre-of-mass energies, lower limits on the Higgs boson masses are set as a function of tan β for several scenarios. For tan β greater than 0.7 they are mh > 84.5 GeV and mA > 86.3 GeV at 95% confidence level.