Avalanche photodiodes (APDs) are the semiconducting analogue of photomultiplier tubes offering very high internal current gain and fast response. APDs are interesting for a wide range of applications in communications1, laser ranging2, biological imaging3, and medical imaging4 where they offer speed and sensitivity superior to those of classical p-n junction-based photodetectors. The APD principle of operation is based on photocurrent multiplication through impact ionization in reverse-biased p-n junctions. APDs can either operate in proportional mode, where the bias voltage is below breakdown, or in Geiger mode, where the bias voltage is above breakdown. In proportional mode, the multiplication gain is finite, thus allowing for photon energy discrimination, while in Geiger mode of operation the multiplication gain is virtually infinite and a self-sustaining avalanche may be triggered, thus allowing detection of single photons5. Here, we demonstrate APDs based on vertically stacked monolayer MoS2 and p-Si, forming an abrupt p-n heterojunction. With this device, we demonstrate carrier multiplication exceeding 1000. Even though such multiplication factors in APDs are commonly accompanied by high noise, our devices show extremely low noise levels comparable with those in regular photodiodes. These heterostructures allow the realization of simple and inexpensive high-performance and low-noise photon counters based on transition metal dichalcogenides.