  We prove that a general (not necessarily symmetric) L\'evy process killed on
exiting a bounded open set (without regular condition on the boundary) is
intrinsically ultracontractive, provided that $B(0,R_0)\subseteq
\rm{supp}(\nu)$ for some constant $R_0>0$, where $\rm{supp}(\nu)$ denotes the
support of the associated L\'evy measure $\nu$. For a symmetric L\'evy process
killed on exiting a bounded H\"older domain of order $0$, we also obtain the
intrinsic ultracontractivity under much weaker assumption on the associated
L\'evy measure.
