  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. 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 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, 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. 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, 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.
