  Models for the progenitor systems of Type Ia supernovae can be divided into
double-degenerate systems, which contain two white dwarfs, and
single-degenerate systems, which contain one white dwarf plus one companion
star (either a red giant, a subgiant, or a >1.16 M_sol main sequence star). The
white dwarf is destroyed in the supernova explosion, but any non-degenerate
companion remains intact. We present the results of a search for an
ex-companion star in SNR 0519-69.0, located in the Large Magellanic Cloud,
based on images taken with the Hubble Space Telescope with a limiting magnitude
of V = 26.05. SNR 0519-69.0 is confidently known to be from a Type Ia supernova
based on its light echoes and X-ray spectra. The geometric center of the
remnant (based on the H-alpha and X-ray shell) is at 05:19:34.83, -69:02:06.92
(J2000). Accounting for the measurement uncertainties, the orbital velocity,
and the kick velocity, any ex-companion star must be within 4.7" of this
position at the 99.73% confidence level. This circle contains 27 main sequence
stars brighter than V = 22.7, any one of which could be the ex-companion star
left over from a supersoft source progenitor system. The circle contains no
post-main sequence stars, and this rules out the possibility of all other
published single-degenerate progenitor classes (including symbiotic stars,
recurrent novae, helium donors, and the spin-up/spin-down models) for this
particular supernova. The only remaining possibility is that SNR 0519-69.0 was
formed from either a supersoft source or a double-degenerate progenitor system.
