  We report the discovery during the Parkes Multibeam Pulsar Survey of PSR
J1756-2251, a 28.5 ms pulsar in a relativistic binary system. Subsequent timing
observations showed the pulsar to have an orbital period of 7.67 hrs and an
eccentricity of 0.18. They also revealed a significant advance of periastron,
2.585+/-0.002 deg./yr. Assuming this is entirely due to general relativity
implies a total system mass (pulsar plus companion) of 2.574+/-0.003 solar
mass. This mass and the significant orbital eccentricity suggest that this is a
double neutron star system. Measurement of the gravitational redshift, gamma,
and an evaluation of the Shapiro delay shape, s, indicate a low companion mass
of <1.25 solar mass. The expected coalescence time due to emission of
gravitational waves is only ~1.7 Gyr substantially less than a Hubble time. We
note an apparent correlation between spin period and eccentricity for normally
evolving double neutron star systems.
