We report the discovery of a new double-image quasar that was found during a search for gravitational lenses in the southern sky. Radio source PMN J1838-3427 is composed of two flat-spectrum components with separation 1.0", flux density ratio 14:1, and matching spectral indices in VLA and VLBA images. Ground-based BRI images show the optical counterpart (total I=18.6) is also double, with the same separation and position angle as the radio components. An HST/WFPC2 image reveals the lens galaxy. The optical flux ratio (27:1) is higher than the radio value, probably because of differential extinction of the components by the lens galaxy. An optical spectrum of the bright component contains quasar emission lines at z=2.78 and several absorption features, including prominent Lyα absorption. The lens galaxy redshift could not be measured, but it is estimated to be z=0.36+/-0.08. The image configuration is consistent with the simplest plausible models for the lens potential. The flat radio spectrum and observed variability of PMN J1838-3427 suggest that the time delay between flux variations of the components is measurable and could thus provide an independent measurement of H0. Based on observations using the Very Large Array (VLA) and Very Long Baseline Array (VLBA) of the National Radio Astronomy Observatory (NRAO), the NASA/ESA Hubble Space Telescope (HST), the 3.6 m telescope of the European Southern Observatory (ESO) at La Silla, the du Pont telescope at Las Campanas Observatory (LCO), and the Australia Telescope Compact Array (ATCA). The NRAO is a facility of the National Science Foundation (NSF) operated under cooperative agreement by Associated Universities for Research in Astronomy, Inc., (AURA). The HST data were obtained from the Space Telescope Science Institute, which is operated by AURA under NASA contract NAS 5-26555. ATCA is part of the Australia Telescope which is funded by the Commonwealth of Australia for operation as a National Facility managed by CSIRO.