In the summer of 2012, during a Pulsar Search Collaboratory workshop, two high-school students discovered J1930$-$1852, a pulsar in a double neutron star (DNS) system. Most DNS systems are characterized by short orbital periods, rapid spin periods and eccentric orbits. However, J1930$-$1852 has the longest spin period ($P_{rm spin}sim$185 ms) and orbital period ($P_{rm b}sim$45 days) yet measured among known, recycled pulsars in DNS systems, implying a shorter than average and/or inefficient recycling period before its companion went supernova. We measure the relativistic advance of periastron for J1930$-$1852, $dot{omega}=0.00078$(4) deg/yr, which implies a total mass (M$_{rm{tot}}=2.59$(4) M$_{odot}$) consistent with other DNS systems. The $2sigma$ constraints on M$_{rm{tot}}$ place limits on the pulsar and companion masses ($m_{rm p}<1.32$ M$_{odot}$ and $m_{rm c}>1.30$ M$_{odot}$ respectively). J1930$-$1852s spin and orbital parameters challenge current DNS population models and make J1930$-$1852 an important system for further investigation.