  The STIS/CCD camera on the {\em Hubble Space Telescope (HST)} was used to
take deep optical images near the K2V main-sequence star $\epsilon$ Eridani in
an attempt to find an optical counterpart of the dust ring previously imaged by
sub-mm observations. Upper limits for the optical brightness of the dust ring
are determined and discussed in the context of the scattered starlight expected
from plausible dust models. We find that, even if the dust is smoothly
distributed in symmetrical rings, the optical surface brightness of the dust,
as measured with the {\em HST}/STIS CCD clear aperture at 55 AU from the star,
cannot be brighter than about 25 STMAG/"$^2$. This upper limit excludes some
solid grain models for the dust ring that can fit the IR and sub-mm data.
Magnitudes and positions for $\approx $59 discrete objects between 12.5" to 58"
from $\epsilon$ Eri are reported. Most if not all of these objects are likely
to be background stars and galaxies.
