  We propose a novel approach to describe the $D^+\to K^+K^-K^+$ decay
amplitude, based on chiral effective Lagrangians, which can be used to extract
information about $K\bar{K}$ scattering. Our trial function is an alternative
to the widely used isobar model and includes both nonresonant three-body
interactions and two-body rescattering amplitudes, based on coupled channels
and resonances, for S- and P-waves with isospin $0$ and $1$. The latter are
unitarized in the $K$-matrix approximation and represent the only source of
complex phases in the problem. Free parameters are just resonance masses and
coupling constants, with transparent physical meanings. The nonresonant
component, given by chiral symmetry as a real polynomium, is an important
prediction of the model, which goes beyond the (2+1) approximation. Our
approach allows one to disentangle the two-body scalar contributions with
different isospins, associated with the $f_0(980)$ and $a_0(980)$ channels. We
show how the $K\bar{K}$ amplitude can be obtained from the decay $D^+\to
K^+K^-K^+$ and discuss extensions to other three-body final states.
