Chordal graphs have been extensively studied and have applications in various fields, including computational biology, sparse matrix computation, and graphical models. They are characterized by the existence of clique trees, whose vertices correspond to the maximal cliques of a chordal graph. In many applications, it is the clique tree of the chordal graph that is of greatest utility. In general, the number of clique trees can grow exponentially with the size of the chordal graph, and in some applications, particular clique trees have greater utility; we want additional criteria to select the most useful clique tree(s). A natural criterion in phylogenetics (and perhaps elsewhere) is that of compactness. In this paper, we formalize this criterion as the average distance between nodes, and present a characterization of clique trees that satisfies this criterion. We also develop a polynomial-time algorithm to find such a clique tree, and show that any minimum average-distance clique tree of a chordal graph can be constructed by our algorithm.