Abstract: A search for the lepton-flavour violating decay D-0 -> e(+/-)mu(-/+) is made with a dataset corresponding to an integrated luminosity of 3.0 fb(-1) of proton-proton collisions at centre-of-mass energies of 7 TeV and 8 TeV, collected by the LHCb experiment. Candidate D-0 mesons are selected using the decay D*(+) -> D-0 pi(+) and the D-0 -> e(+/-)mu(+) branching fraction is measured using the decay mode D-0 -> K-pi(+) as a normalization channel. No significant excess of D-0 -> e(+/-)mu(-/+) candidates over the expected background is seen, and a limit is set on the branching fraction, B(D-0 -> e(+/-)mu(-/+)) < 1.3 x10(-8), at 90% confidence level. This is an order of magnitude lower than the previous limit and it further constrains the parameter space in some leptoquark models and in supersymmetric models with R-parity violation.