A fast algorithm is proposed for the transistor-chaining problem in CMOS functional cell layout based on the layout style of T. Uehara and W.M. van Cleemput (1981). The algorithm takes a transistor-level circuit schematic and outputs a minimum set of transistor chains. Possible diffusion abutments between the transistor pairs are modeled as a bipartite graph. A depth-first search algorithm is used to search for the optimal chaining. Theorems on the set of branches that needs to be explored at each node of the search tree are derived. A theoretical lower bound on the size of the chain set is also derived. This bound enables one to prune the search tree efficiently. The algorithm has been implemented and tested and is able to find optimal solutions almost instantly for all the cases from the literature that were examined.>