We present a search for the rare leptonic decays B+→e+νe and B+→μ+νμ, using the full ϒ(4S) data sample of 772×106 BB¯ pairs collected with the Belle detector at the KEKB asymmetric-energy e+e− collider. One of the B mesons from the ϒ(4S)→BB¯ decay is fully reconstructed in a hadronic mode, while the recoiling side is analyzed for the signal decay. We find no evidence of a signal in any of the decay modes. Upper limits of the corresponding branching fractions are determined as B(B+→e+νe)<3.5×10−6 and B(B+→μ+νμ)<2.7×10−6 at 90% confidence level.Received 25 June 2014DOI:https://doi.org/10.1103/PhysRevD.91.052016© 2015 American Physical Society