We report on a search for CP asymmetry in the singly Cabibbo-suppressed decay D+-> K+K-pi(+) using a data sample of 818 pb(-1) accumulated with the CLEO-c detector on the psi(3770) resonance. A Dalitz-plot analysis is used to determine the amplitudes of the intermediate states. We find no evidence for CP violation either in specific two-body amplitudes or integrated over the entire phase space. The CP asymmetry in the latter case is measured to be (-0.03 +/- 0.84 +/- 0.29)%.