The strange morphology of the six-component gravitational lens PMN J0134 - 0931 has resisted explanation . We present the first successful quantitative models for the system , based on the idea that there are two lens galaxies and two components of the background source . One source is quintuply imaged and corresponds to the five brightest observed radio components . The other source is triply imaged and corresponds to the sixth component , along with two others too faint to have been detected . The models reproduce the observed image positions and fluxes , and make falsifiable predictions about other properties of the system . Some of these predictions have been confirmed by high-resolution radio and optical observations , as described in the companion paper by Winn et al . ( 2003 ) . Although we can not determine the lens model uniquely with current data , we predict that the lens galaxies are spiral galaxies with roughly equal velocity dispersions \sigma \sim 120 \mbox { km~ { } s$ { } ^ { -1 } $ } and a projected separation of only 0 \farcs 4 ( 2 h ^ { -1 } kpc at z _ { l } = 0.76 ) . This system is the first known lens with five images of a single quasar , and the second with more than four images .