A search is performed for a Higgs boson produced in association with a Z boson and decaying into two photons, using the L3 data collected at LEP at a centre-of-mass energy of 189 GeV. All decay modes of the Z are considered. No signal is observed and limits on the branching fraction of the Higgs boson decay into two photons as a function of the Higgs mass are derived assuming a Standard Model production rate. A lower limit on the mass of a fermiophobic Higgs is set at 94.9 GeV at 95% confidence level.