Chemical vapor deposition (CVD) is a powerful method employed for high-quality monolayer crystal growth of 2D transition metal dichalcogenides with much effort invested toward improving the growth process. Here, we report a novel method for CVD-based growth of monolayer molybdenum disulfide (MoS2) by using thermally evaporated thin films of molybdenum trioxide (MoO3) as the molybdenum (Mo) source for coevaporation. Uniform evaporation rate of MoO3 thin films provides uniform Mo vapors which promote highly reproducible single-crystal growth of MoS2 throughout the substrate. These high-quality crystals are as large as 95 μm and are characterized by scanning electron microscopy, Raman spectroscopy, photoluminescence spectroscopy, atomic force microscopy, and transmission electron microscopy. The bottom-gated field-effect transistors fabricated using the as-grown single crystals show n-type transistor behavior with a good on/off ratio of 106 under ambient conditions. Our results presented here address the precursor vapor control during the CVD process and is a major step forward toward reproducible growth of MoS2 for future semiconductor device applications.