  The Hubble Space Telescope WFPC2 camera has been used to image Andromeda III,
a dwarf spheroidal companion (dSph) to M31. The resulting color-magnitude (c-m)
diagrams reveal the morphology of the horizontal branch (HB) in this dwarf
galaxy. We find that like Andromeda I and Andromeda II, and like most of the
Galactic dSph companions, the HB morphology of And III is predominantly red,
redder than that of both And I and And II despite And III having a lower mean
metallicity. We interpret this red HB morphology as indicating that the bulk of
the And III population is ~3 Gyr younger than the age of the majority of
Galactic globular clusters. Nevertheless, the And III c-m diagram does reveal a
few blue HB stars, and a number of RR Lyrae variables are also evident in the
data. This indicates that And III does contain an `old' population of age
comparable to that of the Galactic globular clusters. There is no evidence,
however, for any young stars in And III despite a claimed association between
this dSph and an HI cloud. As was the case for And II, but not And I, no radial
gradient was detected in the And III HB morphology. And III is ~75 kpc from the
center of M31, comparable to the Galactocentric distances of Sculptor and
Draco. Comparison with standard globular cluster red giant branches indicates
<[Fe/H]> = -1.88 +/-0.11, consistent with the absolute-magnitude - mean
abundance relation followed by dSph galaxies. The same comparison yields an
intrinsic abundance dispersion of sigma([Fe/H]) = 0.12, a low value compared to
the Galactic dSphs of comparable luminosity to And III. The list of candidate
variables reveals one definite and one probable Anomalous Cepheid variables.
