A search for a Higgs boson in the four-lepton decay channel H -> ZZ, with each Z boson decaying to an electron or muon pair, is reported. The search covers Higgs boson mass hypotheses in the range of 110 < m(H) < 600 GeV. The analysis uses data corresponding to an integrated luminosity of 4.7 fb(-1) recorded by the CMS detector in pp collisions at root s = 7 TeV from the LHC. Seventy-two events are observed with four-lepton invariant mass m(4l) > 100 GeV (with 13 below 160 GeV), while 67.1 +/- 6.0 (9.5 +/- 1.3) events are expected from background. The four-lepton mass distribution is consistent with the expectation of standard model background production of ZZ pairs. Upper limits at 95% confidence level exclude the standard model Higgs boson in the ranges of 134-158 GeV, 180-305 GeV, and 340-465 GeV. Small excesses of events are observed around masses of 119, 126, and 320 GeV, making the observed limits weaker than expected in the absence of a signal.