One important use of layered semiconductors such as molybdenum disulfide (MoS2) could be in making novel heterojunction devices leading to functionalities unachievable using conventional semiconductors. Here we demonstrate a metal-semiconductor-metal heterojunction photodetector, made of MoS2 and amorphous silicon (a-Si), with rise and fall times of about 0.3 ms. The transient response does not show persistent (residual) photoconductivity, unlike conventional a-Si devices where it may last 3-5 ms, thus making this heterojunction roughly 10X faster. A photoresponsivity of 210 mA/W is measured at green light, the wavelength used in commercial imaging systems, which is 2-4X larger than that of a-Si and best reported MoS2 devices. The device could find applications in large area electronics, such as biomedical imaging, where a fast response is critical.