This article presents differential measurements of the asymmetry between ${\Lambda }_b^0$ $$ {\varLambda}_b^0 $$ and ${\overline{\Lambda }}_b^0$ $$ {\overline{\varLambda}}_b^0 $$ baryon production rates in proton-proton collisions at centre-of-mass energies of $\sqrt{s}$ $$ \sqrt{s} $$ = 7 and 8 TeV collected with the LHCb experiment, corresponding to an integrated luminosity of 3 fb −1. The ${\Lambda }_b^0$ $$ {\varLambda}_b^0 $$ baryons are reconstructed through the inclusive semileptonic decay ${\Lambda }_b^0$ $$ {\varLambda}_b^0 $$ → ${\Lambda }_c^{+}$ $$ {\varLambda}_c^{+} $$ μ − $\overline{\nu }$ $$ \overline{\nu} $$ 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 $\sqrt{s}$ $$ \sqrt{s} $$ = 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.