The first observation of the Z boson decaying to four leptons in proton-proton collisions is presented. The analyzed data set corresponds to an integrated luminosity of 5.02 fb(-1) at root s = 7 TeV collected by the CMS detector at the Large Hadron Collider. A pronounced resonance peak, with a statistical significance of 9.7 sigma, is observed in the distribution of the invariant mass of four leptons (electrons and/or muons) with mass and width consistent with expectations for Z boson decays. The branching fraction and cross section reported here are defined by phase space restrictions on the leptons, namely, 80 < m(4l) < 100 GeV, where m(4l) is the invariant mass of the four leptons, and m(ll) > 4 GeV for all pairs of leptons, where m(ll) is the two-lepton invariant mass. The measured branching fraction is B(Z -> 4(l)) = 4.2(-0.8)(+0.9)(stat.) +/- 0.2(syst.)) x 10(-6) and agrees with the standard model prediction of 4.45 x 10(-6). The measured cross section times branching fraction is sigma(pp -> Z) B (Z -> 4l) = 112(-20)(+23)(stat.) +/-(+7)(-5)(syst.)(-2)(+3) (lumi.) fb, also consistent with the standard model prediction of 120 fb. The four-lepton mass peak arising from Z -> 4l decays provides a calibration channel for the Higgs boson search in the H -> ZZ -> 4l decay mode.