  Type Ia supernovae are understood to arise from the thermonuclear explosion
of a carbon-oxygen white dwarf, yet the evolutionary mechanisms leading to such
events remain unknown. Many proposed channels, including the classical
single-degenerate scenario, invoke a hot, luminous evolutionary phase for the
progenitor, in which it is a prodigious source of photoionizing emission. Here,
we examine the environment of SN 2014J for evidence of a photoionized nebula in
pre- and post-explosion [O III] $\lambda5007$ \AA\ and H$\beta$ images taken
with the Hubble Space Telescope. From the absence of any extended emission, we
exclude a stable nuclear-burning white dwarf at the location of SN 2014J in the
last ~100,000 years, assuming a typical warm interstellar medium (ISM) particle
density of 1 cm$^{-3}$. These limits greatly exceed existing X-ray constraints
at temperatures typical of known supersoft sources. Significant extreme-UV/soft
X-ray emission prior to explosion remains plausible for lower ISM densities
(e.g., $n_{\rm ISM}\sim 0.1~\rm{cm}^{-3}$). In this case, however, any putative
nebula would be even more extended, allowing deeper follow-up observations to
resolve this ambiguity in the near future.
