  The bound state problem of $D^0\bar{D}^{\ast0}$ ($\bar{D}^0{D}^{\ast0}$) is
relevant to the molecular interpretation of the X(3872). We investigated this
problem in a chiral quark model by solving the resonating group method
equation. We found the system is unbound through S-wave $\pi$ and $\sigma$
interactions. The inclusion of $\rho$ and $\omega$ meson exchanges is helpful
to the formation of a molecule. Because the binding energy relies on the
coupling constants, we cannot draw a definite conclusion whether a molecular
state exists in $D^0\bar{D}^{\ast0}$ ($\bar{D}^0{D}^{\ast0}$) system. When
moving on to the bottom counterpart, we obtained an S-wave $B\bar{B}^\ast$
state.
