In this work, we report the discovery and characterization of PSR J1411+2551, a new binary pulsar discovered in the Arecibo 327 MHz Drift Pulsar Survey. Our timing observations of the radio pulsar in the system span a period of about 2.5 years. This timing campaign allowed a precise measurement of its spin period (62.4 ms) and its derivative (9.6 0.7) × 10−20 s s−1; from these, we derive a characteristic age of >9.1 Gyr and a surface magnetic field strength of <2.6 × 109 G. These numbers indicate that this pulsar was mildly recycled by accretion of matter from the progenitor of the companion star. The system has an eccentric (e = 0.17) 2.61 day orbit. This eccentricity allows a highly significant measurement of the rate of advance of periastron, . Assuming general relativity accurately describes the orbital motion, this implies a total system mass M = 2.538 0.022 M . The minimum companion mass is 0.92 M and the maximum pulsar mass is 1.62 M . The large companion mass and the orbital eccentricity suggest that PSR J1411+2551 is a double neutron star system; the lightest known to date including the DNS merger GW170817. Furthermore, the relatively low orbital eccentricity and small proper motion limits suggest that the second supernova had a relatively small associated kick; this and the low system mass suggest that it was an ultra-stripped supernova.