A search for violation of the charge-parity (CP) symmetry in the D+ -> K- K+ pi(+) decay is presented, with proton-proton collision data corresponding to an integrated luminosity of 5.4 fb(-1), collected at a center-of-mass energy of 13 TeV with the LHCb detector. A novel model-independent technique is used to compare the D+ and D- phase-space distributions, with instrumental asymmetries subtracted using the D-s(+) -> K- K+ pi(+) decay as a control channel. The p value for the hypothesis of CP conservation is 8.1%. The CP asymmetry observables A(CP vertical bar S)(phi pi+) = (0.95 +/- 0.43(stat) +/- 0.26(syst)) x 10(-3) and A(CP vertical bar S)((K) over bar *0 K+) = (-0.26 +/- 0.56(stat) +/- 0.18(syst)) x 10(-3) are also measured. These results show no evidence of CP violation and represent the most sensitive search performed through the phase space of a multibody decay.