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A bstract This article presents differential measurements of the asymmetry between $$ {\varLambda}_b^0 $$ Λ b 0 and $$ {\overline{\varLambda}}_b^0 $$ Λ ¯ b 0 baryon production rates in proton-proton collisions at centre-of-mass energies of $$ \sqrt{s} $$ s = 7 and 8 TeV collected with the LHCb experiment, corresponding to an integrated luminosity of 3 fb − 1 . The $$ {\varLambda}_b^0 $$ Λ b 0 baryons are reconstructed through the inclusive semileptonic decay $$ {\varLambda}_b^0 $$ Λ b 0 → $$ {\varLambda}_c^{+} $$ Λ c + μ − $$ \overline{\nu} $$ ν ¯ μ X . The production asymmetry is measured both in intervals of rapidity in the range 2 . 15 < y < 4 . 10 and transverse momentum in 2 < p T < 27 GeV/ c . The results are found to be incompatible with symmetric production with a significance of 5.8 standard deviations for both $$ \sqrt{s} $$ 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 P ythia and heavy-quark recombination are provided. This result constitutes the first observation of a particle-antiparticle asymmetry in b -hadron production at LHC energies.