Monolayer MoSe₂ is a transition metal dichalcogenide with a narrow bandgap, high optical absorbance and large spin-splitting energy, giving it great promise for applications in the field of optoelectronics. Producing monolayer MoSe₂ films in a reliable and scalable manner is still a challenging task as conventional chemical vapor deposition (CVD) or exfoliation based techniques are limited due to the small domains/nanosheet sizes obtained. Here, based on NaCl assisted CVD, we demonstrate the simple and stable synthesis of sub-millimeter size single-crystal MoSe₂ monolayers with mobilities ranging from 38 to 8 cm² V⁻¹ s⁻¹. The average mobility is 12 cm² V⁻¹ s⁻¹. We further determine that the optical responsivity of monolayer MoSe₂ is 42 mA W⁻¹, with an external quantum efficiency of 8.22%.