We report the discovery and initial follow-up of a double neutron star (DNS) system, PSR J1946+2052, with the Arecibo L-Band Feed Array pulsar (PALFA) survey. PSR J1946+2052 is a 17 ms pulsar in a 1.88 hr, eccentric (e = 0.06) orbit with a 1.2 M companion. We have used the Jansky Very Large Array to localize PSR J1946+2052 to a precision of 0 09 using a new phase binning mode. We have searched multiwavelength catalogs for coincident sources but did not find any counterparts. The improved position enabled a measurement of the spin period derivative of the pulsar ( P ˙ = 9 2 × 10 − 19 ); the small inferred magnetic field strength at the surface (BS = 4 × 109 G) indicates that this pulsar has been recycled. This and the orbital eccentricity lead to the conclusion that PSR J1946+2052 is in a DNS system. Among all known radio pulsars in DNS systems, PSR J1946+2052 has the shortest orbital period and the shortest estimated merger timescale, 46 Myr; at that time it will display the largest spin effects on gravitational-wave waveforms of any such system discovered to date. We have measured the advance of periastron passage for this system, ˙ = 25.6 0.3 deg yr − 1 , implying a total system mass of only 2.50 0.04 M , so it is among the lowest-mass DNS systems. This total mass measurement combined with the minimum companion mass constrains the pulsar mass to 1.3 M .