A search is made for the highly-suppressed B meson decays B+→K+K+π− and B+→π+π+K− using a data sample corresponding to an integrated luminosity of 3.0 fb−1 collected by the LHCb experiment in proton–proton collisions at centre-of-mass energies of 7 and 8 TeV. No evidence is found for the decays, and upper limits at 90% confidence level are determined to be B(B+→K+K+π−)<1.1×10−8 and B(B+→π+π+K−)<4.6×10−8.