The synthesis of epitaxially grown, wurtzite CdSe/CdS core/shell nanocrystals is reported. Shells of up to three monolayers in thickness were grown on cores ranging in diameter from 23 to 39 Å. Shell growth was controllable to within a tenth of a monolayer and was consistently accompanied by a red shift of the absorption spectrum, an increase of the room temperature photoluminescence quantum yield (up to at least 50%), and an increase in the photostability. Shell growth was shown to be uniform and epitaxial by the use of X-ray photoelectron spectroscopy (XPS), X-ray diffraction (XRD), high resolution transmission electron microscopy (HRTEM), and optical spectroscopy. The experimental results indicate that in the excited state the hole is confined to the core and the electron is delocalized throughout the entire structure. The photostability can be explained by the confinement of the hole, while the delocalization of the electron results in a degree of electronic accessibility that makes these nanocrystals attractive for use in optoelectronic devices.