  The resonant structure of the doubly Cabibbo-suppressed decay $D^+ \to
K^-K^+K^+$ is studied for the first time. The measurement is based on a sample
of pp-collision data, collected at a centre-of-mass energy of 8 TeV with the
LHCb detector and corresponding to an integrated luminosity of 2 fb$^-1$. The
amplitude analysis of this decay is performed with the isobar model and a
phenomenological model based on an effective chiral Lagrangian. In both models
the S-wave component in the $K^-K^+$ system is dominant, with a small
contribution of the $\phi(1020)$ meson and a negligible contribution from
tensor resonances. The $K^-K^+$ scattering amplitudes for the considered
combinations of spin (0,1) and isospin (0,1) of the two-body system are
obtained from the Dalitz plot fit with the phenomenological decay amplitude.
