Deep X-ray observations of the post-explosion environment around the very nearby Type Ia SN 2014J ( d _ { L } = 3.5 Mpc ) reveal no X-ray emission down to a luminosity L _ { x } < 7 \times 10 ^ { 36 } { erg s ^ { -1 } } ( 0.3-10 keV ) at \delta t \sim 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 \dot { M } < 10 ^ { -9 } { M _ { \sun } y ^ { -1 } } ( for wind velocity v _ { w } = 100 { km s ^ { -1 } } ) . 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 \leq 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 .