  In the framework of RGM, the binding energy of one channel
$\Delta\Delta_{(3,0)}$($d^*$) and $\Delta\Delta_{(0,3)}$ are studied in the
chiral SU(3) quark cluster model. It is shown that the binding energies of the
systems are a few tens of MeV. The behavior of the chiral field is also
investigated by comparing the results with those in the SU(2) and the extended
SU(2) chiral quark models. It is found that the symmetry property of the
$\Delta\Delta$ system makes the contribution of the relative kinetic energy
operator between two clusters attractive. This is very beneficial for forming
the bound dibaryon. Meanwhile the chiral-quark field coupling also plays a very
important role on binding. The S-wave phase shifts and the corresponding
scattering lengths of the systems are also given.
