Type Ia supernovae (SNe Ia) are well-known for their use in the measurement of cosmological distances, but our continuing lack of concrete knowledge about their progenitor stars is both a matter of debate and a source of systematic error. In our attempts to answer this question, we presented unambiguous evidence that LMC SNR 0509-67.5, the remnant of an SN Ia that exploded in the Large Magellanic Cloud 400 +/- 50 years ago, did not have any point sources (stars) near the site of the original supernova explosion, from which we concluded that this particular supernova must have had a progenitor system consisting of two white dwarfs (Schaefer & Pagnotta 2012). There is, however, evidence of nebulosity near the center of the remnant, which could have been left over detritus from the less massive WD, or could have been a background galaxy unrelated to the supernova explosion. We obtained long-slit spectra of the central nebulous region using GMOS on Gemini South to determine which of these two possibilities is correct. The spectra show H-alpha emission at a redshift of z = 0.031, which implies that the nebulosity in the center of LMC SNR 0509-67.5 is a background galaxy, unrelated to the supernova.