Monolayers of transition metal dichalcogenides (TMDCs) are atomically thin direct-gap semiconductors with potential applications in nanoelectronics, optoelectronics, and electrochemical sensing. Recent theoretical and experimental efforts suggest that they are ideal systems for exploiting the valley degrees of freedom of Bloch electrons. For example, Dirac valley polarization has been demonstrated in mechanically exfoliated monolayer MoS2 samples by polarization-resolved photoluminescence, although polarization has rarely been seen at room temperature. Here we report a new method for synthesizing high optical quality monolayer MoS2 single crystals up to 25 μm in size on a variety of standard insulating substrates (SiO2, sapphire, and glass) using a catalyst-free vapor-solid growth mechanism. The technique is simple and reliable, and the optical quality of the crystals is extremely high, as demonstrated by the fact that the valley polarization approaches unity at 30 K and persists at 35% even at room temperature, suggesting a virtual absence of defects. This will allow greatly improved optoelectronic TMDC monolayer devices to be fabricated and studied routinely.