Technological platforms offering efficient integration of III-V semiconductor lasers with silicon electronics are eagerly awaited by industry. The availability of optoelectronic circuits combining III-V light sources with Si-based photonic and electronic components in a single chip will enable, in particular, the development of ultra-compact spectroscopic systems for mass scale applications. The first circuits of such type were fabricated using heterogeneous integration of semiconductor lasers by bonding the III-V chips onto silicon substrates. Direct epitaxial growth of interband III-V laser diodes on silicon substrates has also been reported, whereas intersubband emitters grown on Si have not yet been demonstrated. We report the first quantum cascade lasers (QCLs) directly grown on a silicon substrate. These InAs/AlSb QCLs grown on Si exhibit high performances, comparable with those of the devices fabricated on their native InAs substrate. The lasers emit near 11 µm, the longest emission wavelength of any laser integrated on Si. Given the wavelength range reachable with InAs/AlSb QCLs, these results open the way to the development of a wide variety of integrated sensors.