We perform an analysis of the three-body charmless decay B+ -> K+K+K- using a sample of 226.0 +/- 2.5 million BB pairs collected by the BABAR detector and measure the total branching fraction and CP asymmetry to be B = (35.2 +/- 0.9 +/- 1.6) x 10-6 and A = (-1.7 +/- 2.6 +/- 1.5)%. We fit the Dalitz plot distribution using an isobar model and report the measured values of magnitudes and phases of the production coefficients. The decay dynamics is dominated by the K+K- S-wave, for which we perform a partial-wave analysis in the region m(K+K-) < 2 GeV/c2. We find no evidence of CP violation for individual components of the isobar model.