If Type- ii supernovae – the evolutionary end points of short-lived , massive stars – produce a significant quantity of dust ( > 0.1 M _ { \odot } ) then they can explain the rest-frame far-infrared emission seen in galaxies and quasars in the first Gyr of the Universe . Submillimetre ( submm ) observations of the Galactic supernova remnant , Cas A , provided the first observational evidence for the formation of significant quantities of dust in Type- ii supernovae . In this paper we present new data which show that the submm emission from Cas A is polarised at a level significantly higher than that of its synchrotron emission . The orientation is consistent with that of the magnetic field in Cas A , implying that the polarised submm emission is associated with the remnant . No known mechanism would vary the synchrotron polarisation in this way and so we attribute the excess polarised submm flux to cold dust within the remnant , providing fresh evidence that cosmic dust can form rapidly . This is supported by the presence of both polarised and unpolarised dust emission in the north of the remnant , where there is no contamination from foreground molecular clouds . The inferred dust polarisation fraction is unprecedented ( f _ { pol } \sim 30 per cent ) which , coupled with the brief timescale available for grain alignment ( < 300 yr ) , suggests that supernova dust differs from that seen in other Galactic sources ( where f _ { pol } = 2 - 7 per cent ) , or that a highly efficient grain alignment process must operate in the environment of a supernova remnant .