Recently, two-dimensional layers of transition metal dichalcogenides, such as MoS2, WS2, MoSe2, and WSe2, have attracted much attention for their potential applications in electronic and optoelectronic devices. The selenide analogues of MoS2 and WS2 have smaller band gaps and higher electron mobilities, making them more appropriate for practical devices. However, reports on scalable growth of high quality transition metal diselenide layers and studies of their properties have been limited. Here, we demonstrate the chemical vapor deposition (CVD) growth of uniform MoSe2 monolayers under ambient pressure, resulting in large single crystalline islands. The photoluminescence intensity and peak position indicates a direct band gap of 1.5 eV for the MoSe2 monolayers. A back-gated field effect transistor based on MoSe2 monolayer shows n-type channel behavior with average mobility of 50 cm(2) V(-1) s(-1), a value much higher than the 4-20 cm(2) V(-1) s(-1) reported for vapor phase grown MoS2.