The difference in the angular distributions between beauty quarks and antiquarks, referred to as the charge asymmetry, is measured for the first time in bb pair production at a hadron collider. The data used correspond to an integrated luminosity of 1.0 fb(-1) collected at 7 TeV center-of-mass energy in proton-proton collisions with the LHCb detector. The measurement is performed in three regions of the invariant mass of the bb system. The results obtained are A(C)(bb))(40<M(bb))<75 GeV/c(2)) = 0.4 ± 0.4 ± 0.3%, A(C)(bb))(75<M(bb)) < 105 GeV/c(2)) = 2.0 ± 0.9 ± 0.6%, A(C)(bb)(M(bb)) > 105 GeV/c(2)) = 1.6 ± 1.7 ± 0.6%, where A(C)(bb)) is defined as the asymmetry in the difference in rapidity between jets formed from the beauty quark and antiquark, where in each case the first uncertainty is statistical and the second systematic. The beauty jets are required to satisfy 2 < η < 4, E(T) >20 GeV, and have an opening angle in the transverse plane Δ ϕ > 2.6 rad. These measurements are consistent with the predictions of the standard model.