The T2K Collaboration reports evidence for electron neutrino appearance at the atmospheric mass splitting, |Δm232|≈2.4×10−3  eV2. 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 (3.1σ), and a fit assuming νμ→νe oscillations with sin22θ23=1, δCP=0 and |Δm232|=2.4×10−3  eV2 yields sin22θ13=0.088+0.049−0.039(stat+syst).