One of the problems in the layout of a chemical plant on a single floor is to divide the given set of equipment into sections (groups) of units that reflect the partitions created by aisles or corridors. This is to be accomplished while minimizing the inter-section flow magnitude/cost. By representing the equipment and their connectivities with an edge weighted graph, an analogy to the familiar graph partitioning problem is established. In this paper, a partition of the vertices into subsets of given sizes is sought so as to minimize the total weight of the edges joining vertices from different subsets. We propose a heuristic procedure that has given globally optimal solutions in attractive compulation times to all random graphs studied for which the optimal partitions were obtainable by exhaustive enumeration. This paves the way for obtaining good quality and economical layouts for chemical plants of realistic scope. Extension to the multifloor chemical plant layout problem is discussed.