A type Ia supernova is thought to begin with the explosion of a white dwarf star(1). The explosion could be triggered by the merger of two white dwarfs(2,3) (a 'double-degenerate' origin), or by mass transfer from a companion star(4,5) (the 'single-degenerate' path). The identity of the progenitor is still controversial; for example, a recent argument against the single-degenerate origin(6) has been widely rejected(7-11). One way to distinguish between the double-and single-degenerate progenitors is to look at the centre of a known type Ia supernova remnant to see whether any former companion star is present(12,13). A likely ex-companion star for the progenitor of the supernova observed by Tycho Brahe has been identified(14), but that claim is still controversial(15-18). Here we report that the central region of the supernova remnant SNR 0509-67.5 (the site of a type Ia supernova 400650 years ago, based on its light echo(19,20)) in the Large Magellanic Cloud contains no ex-companion star to a visualmagnitude limit of 26.9 (an absolute magnitude of M(V) = +8.4) within a region of radius 1.43 arcseconds. (This corresponds to the 3 sigma maximum distance to which a companion could have been 'kicked' by the explosion.) This lack of any ex-companion star to deep limits rules out all published single-degenerate models for this supernova. The only remaining possibility is that the progenitor of this particular type Ia supernova was a double-degenerate system.