We report the first room-temperature continuous-wave operation of III-V quantum-dot laser diodes monolithically grown on a Si substrate. Long-wavelength InAs/GaAs quantum-dot structures were fabricated on Ge-on-Si substrates. Room-temperature lasing at a wavelength of 1.28 μm has been achieved with threshold current densities of 163 A/cm(2) and 64.3 A/cm(2) under continuous-wave and pulsed conditions for ridge-waveguide lasers with as cleaved facets, respectively. The value of 64.3 A/cm(2) represents the lowest room-temperature threshold current density for any kind of laser on Si to date.