A first study of CP violation in the decay modes B±→[KS0K±π∓]Dh± and B±→[KS0K∓π±]Dh±, where h labels a K or π meson and D labels a D0 or D-0 meson, is performed. The analysis uses the LHCb data set collected in pp collisions, corresponding to an integrated luminosity of 3 fb-1. The analysis is sensitive to the CP-violating CKM phase γ through seven observables: one charge asymmetry in each of the four modes and three ratios of the charge-integrated yields. The results are consistent with measurements of γ using other decay modes. © 2014 The Authors.