It is argued that fusion chain reactions in the D-D system is feasible with supra-thermal deuterons in the MeV regime, with new generations of deuterons being generated either via neutron–deuteron or proton–deuteron collisions. The propagation of supra-thermal deuterons in an infinite, hot, dense deuterium target was studied using a Monte Carlo method that includes multiple nuclear reactions, electron and ion stopping, along with neutron and proton knock-ons. Over a wide range of densities we observed significant, albeit sub-critical chain reactions in the multi-keV temperature regime. At very high densities (over 1000 gcm−3) and temperatures (over 40 keV) we observed chain reactions that reached criticality. These results suggest that there is a case to re-assess the potential of inertial confinement fusion based on deuterium-heavy targets.