We report the growth of a new closely lattice-matched II-VI heterostructure: ZnTe/CdSe (Δa/a∼0.3%). Epilayers of zinc blende CdSe grown on ZnTe buffer layers are shown to have much better quality than those grown earlier (with a 7% mismatch) on GaAs substrates. This permitted the first successful growth of high quality superlattices of ZnTe/CdSe. The superlattices were studied by x-ray diffraction, transmission electron microscopy, and optical techniques. Results of photoluminescence and optical transmission measurements show that ZnTe/CdSe superlattices have a very small valence-band offset.