  The charmless decays $B^{\pm}\to K^{\pm}\pi^+\pi^-$ and $B^{\pm}\to
K^{\pm}K^+K^-$ 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 $A_{C\!P}(B^{\pm}\to
K^{\pm}\pi^+\pi^-) = 0.032 \pm 0.008 \stat \pm 0.004 \syst \pm 0.007 (J\psi
K^{\pm})$ and $A_{C\!P}(B^{\pm}\to K^{\pm}K^+K^-) = -0.043 \pm 0.009 \stat \pm
0.003 \syst \pm 0.007 (J\psi K^{\pm})$, where the third uncertainty is due to
the $C\!P$ asymmetry of the $B^{\pm}\to J\psi K^{\pm}$ reference mode. The
significance of $A_{C\!P}(B^{\pm}\to K^{\pm}K^+K^-)$ exceeds three standard
deviations and is the first evidence of an inclusive $C\!P$ asymmetry in
charmless three-body $B$ decays. In addition to the inclusive $C\!P$
asymmetries, larger asymmetries are observed in localised regions of phase
space.
