The highest level in the hierarchy of protein structure and folding is the formation of protein complexes through protein-protein interactions. We have made modifications to a well established computer lattice model to expand its applicability to two-protein dimerization and aggregation. Based on Brownian dynamics, we implement translation and rotation moves of two peptide chains relative to each other, in addition to the intrachain motions already present in the model. We use this two-chain model to study the folding dynamics of the yeast transcription factor GCN4 leucine zipper. The calculated heat capacity curves agree well with experimental measurements. Free energy landscapes and median first passage times for the folding process are calculated and elucidate experimentally measured characteristics such as the multistate nature of the dimerization process.