We report here the Einstein@Home discovery of PSR J1913+1102, a 27.3-ms pulsar found in data from the ongoing Arecibo PALFA pulsar survey. The pulsar is in a 4.95-hr double neutron star (DNS) system with an eccentricity of 0.089. From radio timing with the Arecibo 305-m telescope, we measure the rate of advance of periastron to be 5.632(18) deg/yr. Assuming general relativity accurately models the orbital motion, this corresponds to a total system mass of 2.875(14) solar masses, similar to the mass of the most massive DNS known to date, B1913+16, but with a much smaller eccentricity. The small eccentricity indicates that the second-formed neutron star (the companion of PSR J1913+1102) was born in a supernova with a very small associated kick and mass loss. In that case this companion is likely, by analogy with other systems, to be a light (1.2 solar mass) neutron star; the system would then be highly asymmetric. A search for radio pulsations from the companion yielded no plausible detections, so we can't yet confirm this mass asymmetry. By the end of 2016, timing observations should permit the detection of two additional post-Keplerian parameters: the Einstein delay, which will enable precise mass measurements and a verification of the possible mass asymmetry of the system, and the orbital decay due to the emission of gravitational waves, which will allow another test of the radiative properties of gravity. The latter effect will cause the system to coalesce in ~0.5 Gyr.