  The $DK$ interaction is relevant to the interpretation of the $D_{sJ}(2317)$.
We dynamically investigate $S$-wave $DK$ interactions in the chiral SU(3) quark
model by solving the resonating group method equation. The numerical results
show an attraction between $D$ and $K$, which is from boson exchanges between
light quarks. However, such an attraction is not strong enough to form a $DK$
molecule. Meanwhile, $S$ partial wave phase shifts of $DK$ elastic scattering
are obtained. The case of $S$-wave $D^*K$ is rather similar to that of $DK$. To
draw a definite conclusion whether a molecular state exists in $DK$ or $D^*K$
system, more details of dynamics should be considered in further study.
