Deep X-ray observations of the post-explosion environment around the very nearby Type Ia SN 2014J (d sub(L) = 3.5 Mpc) reveal no X-ray emission down to a luminosity L sub(x) < 7 x 10 super(36) erg s super(-1) (0.3-10 keV) at delta 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 M < 10 super(-9) M sub(middot in circle) yr super(-1) (for wind velocity v sub(w) = 100 km s super(-1)). Alternatively, the SN shock might be expanding into a uniform medium with density n sub(CSM) < 3 cm super(-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 < or =, slant 1 %. The allowed progenitors are (1) white dwarf-white dwarf progenitors, (2) SD systems with unstable hydrogen burning experiencing recurrent nova eruptions with recurrence time t < 300 yr, and (3) stars where the mass loss ceases before the explosion.