Doctor of Philosophy / Department of Physics / Yurii Y. Maravin / This thesis presents the first study of a rare production of Z boson in association with two photons (Zγγ), where the Z boson decays into a pair of muons or electrons, by proton-proton collisions at the Large Hadron Collider (LHC). This study uses full data samples that have been collected with the Compact Muon Solenoid (CMS) detector in 2012 with a center of mass energy of 8TeV, corresponding to an integrated luminosity of 19.7 fb⁻¹. The Zγγ production cross section is measured within a fiducial region defined by two leptons with two photons where transverse momentum over 15 GeV and distance between gamma and lepton above 0.4. Using the obtained samples, the Zγγ cross section is measured to be: 12.6 ±1.6 (stat.) ± 1.7 (syst.) ± 0.3 (lumi.) fb. where stat., syst., and lumi. denote the statistical uncertainty, systematic uncertainty, and the uncertainty in integrated luminosity, respectively. This result is in an excellent agreement with the theoretical prediction of 13.0 ± 1.5 fb.