The T2K Collaboration reports evidence for electron neutrino appearance at the atmospheric mass splitting, vertical bar Delta m(32)(2)vertical bar approximate to 2.4 X 10(-3) eV(2). An excess of electron neutrino interactions over background is observed from a muon neutrino beam with a peak energy of 0.6 GeV at the Super-Kamiokande (SK) detector 295 km from the beam's origin. Signal and background predictions are constrained by data from near detectors located 280 m from the neutrino production target. We observe 11 electron neutrino candidate events at the SK detector when a background of 3.3 +/- 0.4(syst) events is expected. The background-only hypothesis is rejected with a p value of 0.0009 (3.1 sigma), and a fit assuming nu(mu) -> nu(e) oscillations with sin (2)2 theta(23) = 1, delta(CP) = 0 and vertical bar Delta m(32)(2)vertical bar = 2.4 X 10(-3) eV(2) yields sin (2)2 theta(13) = 0.088(-0.039)(+0.049)(stat + syst).