It is well-known that any chordal graph can be represented as a clique tree (acyclic hypergraph, join tree). Since some chordal graphs have many distinct clique tree representations, it is interesting to consider which one is most desirable under various circumstances. A clique tree of minimum diameter (or height) is sometimes a natural candidate when choosing clique trees to be processed in a parallel computing environment. This paper introduces a linear time algorithm for computing a minimum-diameter clique tree. The new algorithm is an analogue of the natural greedy algorithm for rooting an ordinary tree in order to minimize its height. It has potential application in the development of parallel algorithms for both knowledge-based systems and the solution of sparse linear systems of equations. 31 refs., 7 figs.