Simultaneous observations of microlensing events from multiple locations allow for the breaking of degeneracies between the physical properties of the lensing system, specifically by exploring different regions of the lens plane and by directly measuring the "microlens parallax." We report the discovery of a 30-65M(J) brown dwarf orbiting a K dwarf in the microlensing event OGLE-2015-BLG-1319. The system is located at a distance of similar to 5 kpc toward the Galactic Bulge. The event was observed by several ground-based groups as well as by Spitzer and Swift, allowing a measurement of the physical properties. However, the event is still subject to an eight-fold degeneracy, in particular the well-known close-wide degeneracy, and thus the projected separation between the two lens components is either similar to 0.25 au or similar to 45 au. This is the first microlensing event observed by Swift, with the UVOT camera. We study the region of microlensing parameter space to which Swift is sensitive, finding that though Swift could not measure the microlens parallax with respect to ground-based observations for this event, it can be important for other events. Specifically, it is important for detecting nearby brown dwarfs and free-floating planets in high magnification events.