We report the synthesis of a series of nearly monodisperse ZnS-overcoated CdSe quantum dots whose room temperature photoluminescence quantum yield approaches 50%. This spectrally narrow (FWHM < 40nm) band edge luminescence spans the visible region from blue to red light. We use a two-step synthesis based on the high temperature decomposition of organometallic precursors in a coordinating solvent. We characterize our composite quantum dots using optical spectroscopies, wavelength dispersive x-ray spectroscopy, x-ray photoelectron spectroscopy, high resolution transmission electron microscopy, small angle x-ray scattering, and wide angle x-ray diffraction. The data indicate that samples displaying the highest quantum yield are those which have just achieved a closed shell of ZnS encapsulating the CdSe core. As more ZnS is added, the quantum yield decreases somewhat, possibly due to the many defects present in larger ZnS shells.