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The production of the charm-strange baryon Ξc0 is measured for the first time at the LHC via its semileptonic decay into eΞ−+νe in pp collisions at s=7 TeV with the ALICE detector. The transverse momentum (pT) differential cross section multiplied by the branching ratio is presented in the interval 1<pT<8 GeV/c at mid-rapidity, |y|<0.5. The transverse momentum dependence of the Ξc0 baryon production relative to the D0 meson production is compared to predictions of event generators with various tunes of the hadronisation mechanism, which are found to underestimate the measured cross-section ratio.