A search for the lepton-flavor-violating decays B0s→e±μ∓ and B0→e±μ∓ is performed with a data sample, corresponding to an integrated luminosity of 1.0 fb−1 of pp collisions at s√=7 TeV, collected by the LHCb experiment. The observed number of B0s→e±μ∓ and B0→e±μ∓ candidates is consistent with background expectations. Upper limits on the branching fractions of both decays are determined to be B(B0s→e±μ∓)<1.1(1.4)×10−8 and B(B0→e±μ∓)<2.8(3.7)×10−9 at 90% (95%) confidence level (C.L.). These limits are a factor of 20 lower than those set by previous experiments. Lower bounds on the Pati-Salam leptoquark masses are also calculated, MLQ(B0s→e±μ∓)>101 TeV/c2 and MLQ(B0→e±μ∓)>126 TeV/c2 at 95% C.L., and are a factor of 2 higher than the previous bounds.