A type Ia supernova is thought to begin with the explosion of a white dwarf star. The explosion could be triggered by the merger of two white dwarfs (a `double-degenerate' origin), or by mass transfer from a companion star (the `single-degenerate' path). The identity of the progenitor is still controversial; for example, a recent argument against the single-degenerate origin has been widely rejected. 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. A likely ex-companion star for the progenitor of the supernova observed by Tycho Brahe has been identified, but that claim is still controversial. Here we report that the central region of the supernova remnant SNR 0509-67.5 (the site of a type Ia supernova 400 +/- 50 years ago, based on its light echo) in the Large Magellanic Cloud contains no ex-companion star to a visual magnitude limit of 26.9 (an absolute magnitude of MV = +8.4) within a region of radius 1.43 arcseconds. (This corresponds to the 3σ 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.