The discovery of a radioactively powered kilonova associated with the binary neutron star merger GW170817 was the first—and still only—confirmed electromagnetic counterpart to a gravitational-wave event [ 1 , 2 ] . However , observations of late-time electromagnetic emission are in tension with the expectations from standard neutron-star merger models . Although the large measured ejecta mass [ 3 , 4 ] is potentially explained by a progenitor system that is asymmetric in terms of the stellar component masses , i.e . with a mass ratio q of 0.7–0.8 [ 5 ] , the known Galactic population of merging double neutron star ( DNS ) systems ( i.e . those that will coalesce within billions of years or less ) has , until now , only consisted of nearly equal-mass ( q > 0.9 ) binaries [ 6 ] . PSR J1913+1102 is a DNS system in a 5-hour , low-eccentricity ( e = 0.09 ) orbit , implying an orbital separation of 1.8 solar radii [ 7 ] , with the two neutron stars predicted to coalesce in 470 million years due to gravitational-wave emission . Here we report that the masses of the two neutron stars , as measured by a dedicated pulsar timing campaign , are 1.62 \pm 0.03 and 1.27 \pm 0.03 solar masses for the pulsar and companion neutron star , respectively ; with a measured mass ratio q = 0.78 \pm 0.03 , it is the most asymmetric DNS among known merging systems . Based on this detection , our population synthesis analysis implies that such asymmetric binaries represent between 2 and 30 % ( 90 % confidence ) of the total population of merging DNS binaries . The coalescence of a member of this population offers a possible explanation for the anomalous properties of GW170817 , including the observed kilonova emission from that event .