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Abstract: We report the discovery of PSR J1753-2240 in the Parkes Multibeam Pulsar Survey database. This 95-ms pulsar is in an eccentric binary system with a 13.6-day orbital period. Period derivative measurements imply a characteristic age in excess of 1 Gyr, suggesting that the pulsar has undergone an episode of accretion-induced spin-up. The eccentricity and spin period are indicative of the companion being a second neutron star, so that the system is similar to that of PSR J1811-1736, although other companion types cannot be ruled out at this time. The companion mass is constrained by geometry to lie above 0.48 solar masses, although long-term timing observations will give additional constraints. If the companion is a white dwarf or main sequence star, optical observations may yield a direct detection of the companion. If the system is indeed one of the few known double neutron star systems, it would lie significantly far from the recently proposed spin-period/eccentricity relationship.