Molecular beam epitaxy has been used to grow single-crystal bcc Co/Fe multilayers on GaAs(110BAR) and MgO(001). The influence of the substrate and its temperature on the formation of bcc Co has been examined. The crystal quality and thickness stability limits for this metastable phase are significantly improved with respect to samples grown by rf sputtering. The presence of Fe epilayer and its thickness are found to be critical in the stabilization of bcc Co.