  We present a chiral model for the $J=0, I=1/2,$ elastic $K\p$ amplitude,
suited to be employed in $D^+ \rar K^- \p^+ \p^+$ data analyses and valid
between threshold and $1.5 $GeV. Although not as precise as other versions
available in the literature, it is rather simple and incorporates the essential
physics in this energy domain. In the case of the $K$-matrix approximation, the
model allows the pole structure of the $K\p$ amplitude to be understood by
solving a quadratic equation in $s$. We show that the solutions to this
equation can be well approximated by polynomials of masses and coupling
constants. This analytic structure allows a clear understanding why, depending
on the values of one of the coupling constants, one may have one or two
physical poles. The model yields a pole, associated with the $\k$, at
$\sqrt{s}= (0.75 - i 0.24) $GeV.
