To understand the nature of supernovae and neutron star ( NS ) formation , as well as binary stellar evolution and their interactions , it is important to probe the distribution of NS masses . Until now , all double NS ( DNS ) systems have been measured to have a mass ratio close to unity ( q \geq 0.91 ) . Here we report the measurement of the individual masses of the 4.07-day binary pulsar J0453+1559 from measurements of the rate of advance of periastron and Shapiro delay : The mass of the pulsar is M _ { p } = 1.559 \pm 0.005 \mathrm { M _ { \sun } } and that of its companion is M _ { c } = 1.174 \pm 0.004 \mathrm { M _ { \sun } } ; q = 0.75 . If this companion is also a neutron star ( NS ) , as indicated by the orbital eccentricity of the system ( e = 0.11 ) , then its mass is the smallest precisely measured for any such object . The pulsar has a spin period of 45.7 ms and a spin period derivative \dot { P } = ( 1.8616 \pm 0.0007 ) \times 10 ^ { -19 } s~ { } s ^ { -1 } ; from these we derive a characteristic age of \sim 4.1 \times 10 ^ { 9 } years and a magnetic field of \sim 2.9 \times 10 ^ { 9 } G , i.e , this pulsar was mildly recycled by accretion of matter from the progenitor of the companion star . This suggests that it it was formed with ( very approximately ) its current mass . Thus NSs form with a wide range of masses , which is important for understanding their formation in supernovae . It is also important for the search for gravitational waves released during a NS-NS merger : it is now evident that we should not assume all DNS systems are symmetric .