  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 cannot determine the lens model uniquely with current
data, we predict that the lens galaxies are spiral galaxies with roughly equal
velocity dispersions sigma~120km/s and a projected separation of only 0.4" (2/h
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.
