A search for a Higgs boson produced in e+e− collisions in association with a Z boson and decaying into invisible particles is performed. Data collected at LEP with the L3 detector at centre-of-mass energies from 189 to 209 GeV are used, corresponding to an integrated luminosity of 0.63 fb−1. Events with hadrons, electrons or muons with visible masses compatible with a Z boson and missing energy and momentum are selected. They are consistent with the Standard Model expectations. A lower limit of 112.3 GeV is set at 95% confidence level on the mass of the invisibly-decaying Higgs boson in the hypothesis that its production cross section equals that of the Standard Model Higgs boson. Relaxing this hypothesis, upper limits on the production cross section are derived.