The cross section α(e(+)e(-) → π(+)π(-)-γ) has been measured with the KLOE detector at the electron-positron collider DAΦ NE, at an energy W = mφ = 1.02 GeV. We perform this measurement as a function of the π(+)π(-) invariant mass, M-ππ. The photon in the above process is due to Initial State Radiation. Dividing by a theoretical radiator function, we obtain the cross section α(e(+)e(-) - π(+)π(-)) for the mass range 0.35 < M-ππ(2) < 0.95 GeV2 with an overall accuracy of 1.3%. We also calculate the hadronic contribution of the two-pion channel to the anomalous magnetic moment of the muon for the given mass range: α(ππ)(μ) = (388.7 ± 0.8(stat) ± 3.5(syst) ± 3.5(theo)). 10(-10).