  Deep X-ray observations of the post-explosion environment around the very
nearby Type Ia SN\,2014J (Dl=3.5 Mpc) reveal no X-ray emission down to a
luminosity L<7x10^{36} erg/s (0.3-10 keV) at t~20 days after the explosion. We
interpret this limit in the context of Inverse Compton emission from
upscattered optical photons by the supernova shock and constrain the
pre-explosion mass-loss rate of the stellar progenitor system to be <10^{-9}
M_sun yr-1 (for wind velocity v_w=100 km/s). Alternatively, the SN shock might
be expanding into a uniform medium with density $n_CSM<3 cm-3. These results
rule out single-degenerate (SD) systems with steady mass-loss until the
terminal explosion and constrain the fraction of transferred material lost at
the outer Lagrangian point to be <1%. The allowed progenitors are (i) WD-WD
progenitors, (ii) SD systems with unstable hydrogen burning experiencing
recurrent nova eruptions with recurrence time t<300 yrs and (iii) stars where
the mass loss ceases before the explosion.
