  Within the framework of QCD sum rules, we have investigated the tetraquark
states with three heavy quarks. We systematically construct the interpolating
currents for the possible $cc\bar{c}\bar{q}$, $cc\bar{b}\bar{q}$,
$bc\bar{b}\bar{q}$, $bb\bar{b}\bar{q}$ tetraquark states with quantum numbers
$J^{P}=0^{+}$ and $J^{P}=1^{+}$. Using these interpolating currents, we have
calculated the two-point correlation functions and extracted the mass spectra
for the above tetraquark states. We also discuss the decay patterns of these
tetraquarks, and notice that the $cc\bar{c}\bar{q}$, $cc\bar{b}\bar{q}$,
$bc\bar{b}\bar{q}$ may decay quickly with a narrow width due to their mass
spectra. The $bb\bar{b}\bar{q}$ tetraquarks are expected to be very narrow
resonances since their OZI-allowed decay modes are kinematically forbidden.
These states may be searched for in the final states with a $B$ meson plus a
light meson or photon.
