  A \textit{distinguishing coloring} of a graph $G$ is a coloring of the
vertices so that every nontrivial automorphism of $G$ maps some vertex to a
vertex with a different color. The \textit{distinguishing number} of $G$ is the
minimum $k$ such that $G$ has a distinguishing coloring where each vertex is
assigned a color from $\{1,\ldots,k\}$. A \textit{list assignment} to $G$ is an
assignment $L=\{L(v)\}_{v\in V(G)}$ of lists of colors to the vertices of $G$.
A \textit{distinguishing $L$-coloring} of $G$ is a distinguishing coloring of
$G$ where the color of each vertex $v$ comes from $L(v)$. The {\it list
distinguishing number} of $G$ is the minimum $k$ such that every list
assignment to $G$ in which $|L(v)|=k$ for all $v\in V(G)$ yields a
distinguishing $L$-coloring of $G$. We prove that if $G$ is an interval graph,
then its distinguishing number and list distinguishing number are equal.
