The Drell-Yan differential cross section is measured in pp collisions at sqrt(s) = 7 TeV, from a data sample collected with the CMS detector at the LHC, corresponding to an integrated luminosity of 36 inverse picobarns. The cross section measurement, normalized to the measured cross section in the Z region, is reported for both the dimuon and dielectron channels in the dilepton invariant mass range 15-600 GeV. The normalized cross section values are quoted both in the full phase space and within the detector acceptance. The effect of final state radiation is also identified. The results are found to agree with theoretical predictions.