A first measurement of the cross section of the process e+e−→Zγγ is reported using a total integrated luminosity of 231 pb−1 collected with the L3 detector at centre-of-mass energies of 182.7 GeV and 188.7 GeV. By selecting hadronic events with two isolated photons the e+e−→Zγγ cross section is measured to be0.49 -0.20/-0.17 ±0.04 pb at182.7 GeV and 0.47±0.10±0.04pb at 188.7 GeV. The measurements are consistent with Standard Model expectations. Limits on Quartic Gauge Boson Couplings a0/Λ2 and ac/Λ2 of -0.009 GeV-2<α0/ᴧ2<0.008 GeV-2 and -0.007 GeV-2<αc/ᴧ2<0.013 GeV-2 are derived at 95% confidence level.