A search for the Standard Model Higgs boson has been performed with the L3 detector at LEP. The data sample was collected at three centre-of-mass energies, 161.3, 170.3 and 172.3 GeV with integrated luminosities of 10.8, 1.0 and 9.2 pb, respectively. No Higgs signal is observed. In combination with previous data taken at the Z resonance, a lower Higgs mass limit, MH > 69.5 GeV, is obtained at 95% confidence level.