  We study the chiral interactions of the hidden charm $D\bar{D}^*$ system
within chiral effective field theory. Chiral Lagrangians are constructed by
incorporating the chiral symmetry, heavy quark symmetry as well as proper
charge conjugation properties of the heavy mesons. The interacting potentials
of the $S$-wave $D\bar{D}^*$ are calculated up to second chiral order at 1-loop
level, where complete two-pion exchange interactions are included. We further
investigate the behaviors of the potentials in coordinate space, as well as
their bound state properties. Our studies indicate that there exists a
interacting strength ordering among considered four channels:
$\text{str.}[0^+(1^{++})]>\text{str.}[0^-(1^{+-})] > \text{str.}[1^+(1^{+-})] >
\text{str.}[1^-(1^{++})]$ where str. stands for the strength of the
$D\bar{D}^*$ interaction. Moreover, we find that $X(3872)$ can be treated as a
good candidate of $0^+(1^{++})$ molecular state. There also tends to form
$0^-(1^{+-})$ and $1^+(1^{+-})$ molecular states and we expect the experiments
to search for the predicted multi-structures around the $D\bar{D}^*$ mass
region.
