This article presents differential measurements of the asymmetry between Λ0b and Λ¯¯¯¯0b baryon production rates in proton-proton collisions at centre-of-mass energies of s√ = 7 and 8 TeV collected with the LHCb experiment, corresponding to an integrated luminosity of 3 fb−1. The Λ0b baryons are reconstructed through the inclusive semileptonic decay Λ0b → Λ+cμ−ν¯¯¯μX. The production asymmetry is measured both in intervals of rapidity in the range 2.15 < y < 4.10 and transverse momentum in 2 < pT < 27 GeV/c. The results are found to be incompatible with symmetric production with a significance of 5.8 standard deviations for both s√ = 7 and 8 TeV data, assuming no CP violation in the decay. There is evidence for a trend as a function of rapidity with a significance of 4 standard deviations. Comparisons to predictions from hadronisation models in PYTHIA and heavy-quark recombination are provided. This result constitutes the first observation of a particle-antiparticle asymmetry in b-hadron production at LHC energies.