The charmless decays B±→K±π+π− and B±→K±K+K− are reconstructed using data, corresponding to an integrated luminosity of 1.0  fb−1, collected by LHCb in 2011. The inclusive charge asymmetries of these modes are measured as ACP(B±→K±π+π−)=0.032±0.008 (stat)±0.004 (syst)±0.007(J/ψK±) and ACP(B±→K±K+K−)=−0.043±0.009 (stat)±0.003 (syst)±0.007(J/ψK±), where the third uncertainty is due to the CP asymmetry of the B±→J/ψK± reference mode. The significance of ACP(B±→K±K+K−) exceeds three standard deviations and is the first evidence of an inclusive CP asymmetry in charmless three-body B decays. In addition to the inclusive CP asymmetries, larger asymmetries are observed in localized regions of phase space.