The charmless decays B± → K+ K- π± and B± → π+ π- π± are reconstructed in a data set of pp collisions with an integrated luminosity of 1.0 fb(-1) and center-of-mass energy of 7 TeV, collected by LHCb in 2011. The inclusive charge asymmetries of these modes are measured to be A(CP)(B± → K+ K- π±) = -0.141±0.040 (stat)±0.018 (syst)±0.007(J/ψ K±) and A(CP)(B± → π+ π- π±) = 0.117±0.021 (stat)±0.009 (syst)±0.007(J/ψ K±), where the third uncertainty is due to the CP asymmetry of the B± → J/ψK± reference mode. In addition to the inclusive CP asymmetries, larger asymmetries are observed in localized regions of phase space.