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.
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