  Hubble Space Telescope observations of the gravitational lens PG 1115+080 in
the infrared show the known z =0.310 lens galaxy and reveal the z = 1.722
quasar host galaxy. The main lens galaxy G is a nearly circular (ellipticity <
0.07) elliptical galaxy with a de Vaucouleurs profile and an effective radius
of R_e = 0.59 +/- 0.06 arcsec (1.7 +/- 0.2 h^{-1} kpc for Omega = 1 and h =
H_0/100 km/s/Mpc). G is part of a group of galaxies that is a required
component of all successful lens models. The new quasar and lens positions (3
milliarcsecond errors) yield constraints for these models that are
statistically degenerate, but several conclusions are firmly established. (1)
The principal lens galaxy is an elliptical galaxy with normal structural
properties, lying close to the fundamental plane for its redshift. (2) The
potential of the main lens galaxy is nearly round, even when not constrained by
the small ellipticity of the light of this galaxy. (3) All models involving two
mass distributions place the group component near the luminosity-weighted
centroid of the brightest nearby group members. (4) All models predict a time
delay ratio r_{ABC} = 1.3. (5) Our lens models predict H_0 = 44 +/- 4 km/s/Mpc
if the lens galaxy contains dark matter and has a flat rotation curve, and H_0
= 65 +/- 5 km/s/Mpc if it has a constant mass-to-light ratio. (6) Any dark halo
of the main lens galaxy must be truncated near 1.5 arcsec (4 h^{-1} kpc) before
the inferred Ho rises above 60 km/s/Mpc. (7) The quasar host galaxy is lensed
into an Einstein ring connecting the four quasar images, whose shape is
reproduced by the models. Improved NICMOS imaging of the ring could be used to
break the degeneracy of the lens models.
