  The possibility of $QQ\bar{q}\bar{q}$ heavy-light four-quark bound states has
been analyzed by means of the chiral SU(3) quark model, where $Q$ is the heavy
quark ($c$ or $b$) and $q$ is the light quark ($u$, $d$ or $s$). We obtain a
bound state for the $bb\bar{n}\bar{n}$ configuration with quantum number
$J^{P}=1^{+},I=0$ and for the $cc\bar{n}\bar{n}$ ($J^{P}=1^{+},I=0$)
configuration which is not bound but slightly above the $D^{*}D^{*}$ threshold
(n is $u$ or $d$ quark). Meanwhile, we also conclude that a weakly bound state
in $bb\bar{n}\bar{n}$ system can also be found without considering the chiral
quark interactions between the two light quarks, yet its binding energy is
weaker than that with the chiral quark interactions.
