Monolayer transition-metal dichalcogenides (TMDs) have the potential to become efficient optical-gain materials for low-energy-consumption nanolasers with the smallest gain media because of strong excitonic emission. However, until now TMD-based lasing has been realized only at low temperatures. Here we demonstrate for the first time a room-temperature laser operation in the infrared region from a monolayer of molybdenum ditelluride on a silicon photonic-crystal cavity. The observation is enabled by the unique combination of a TMD monolayer with an emission wavelength transparent to silicon, and a high-Q cavity of the silicon nanobeam. The laser is pumped by a continuous-wave excitation, with a threshold density of 6.6 W cm-2. Its linewidth is as narrow as 0.202 nm with a corresponding Q of 5,603, the largest value reported for a TMD laser. This demonstration establishes TMDs as practical materials for integrated TMD-silicon nanolasers suitable for silicon-based nanophotonic applications in silicon-transparent wavelengths.