This article presents differential measurements of the asymmetry between Lambda(0)(b) and (Lambda) over bar (0)(b) baryon production rates in proton-proton collisions at centre-of-mass energies of root s = 7 and 8 TeV collected with the LHCb experiment, corresponding to an integrated luminosity of 3 fb(-1). The Lambda(0)(b) baryons are reconstructed through the inclusive semileptonic decay Lambda(0)(b) -> Lambda(+)(c) mu(-)(nu) over bar X-mu. 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 root 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.