  The explosion of a Type Ia supernova, SN 2011ef, in the nearby Pinwheel
galaxy (M101 at 6.4 Mpc) provides an opportunity to study pre-explosion images
and search for the progenitor, which should consist of a white dwarf (WD),
possibly surrounded by an accretion disk, in orbit with another star. We report
on our use of deep Chandra observations to limit the luminosity and temperature
of the pre-explosion white dwarf (WD). It is found that if the spectrum was a
blackbody, then WDs of highest possible temperatures and luminosities are
excluded but, even if the WD was emitting at the Eddington luminosity, values
of kT less than roughly 60 eV are permitted. This allows the progenitor to be
an accreting nuclear-burning WD with an expanded photosphere. Pre-SN HST
observations were used to derive a lower limit of about 10 eV for the expanded
photosphere. Li et al.\, (2011) have already ruled out the possibility of a
giant donor. We consider the combined emission from the WD, disk, and donor,
and find that even the combined emission from a bright subgiant, WD and disk
would not likely have been observed prior to explosion, and neither would some
local candidates for the nuclear-burning WD model.
