  High precision radial velocity (RV) measurements spanning the years
1980.8--2000.0 are presented for the nearby (3.22 pc) K2 V star $\epsilon$ Eri.
These data, which represent a combination of six independent data sets taken
with four different telescopes, show convincing variations with a period of
$\approx$ 7 yrs. A least squares orbital solution using robust estimation
yields orbital parameters of period, $P$ = 6.9 yrs, velocity $K$-amplitude $=$
19 {\ms}, eccentricity $e$ $=$ 0.6, projected companion mass $M$ sin $i$ = 0.86
$M_{Jupiter}$, and semi-major axis $a_2$ $=$ 3.3 AU. Ca II H&K S-index
measurements spanning the same time interval show significant variations with
periods of 3 and 20 yrs, yet none at the RV period. If magnetic activity were
responsible for the RV variations then it produces a significantly different
period than is seen in the Ca II data. Given the lack of Ca II variation with
the same period as that found in the RV measurements, the long-lived and
coherent nature of these variations, and the high eccentricity of the implied
orbit, Keplerian motion due to a planetary companion seems to be the most
likely explanation for the observed RV variations. The wide angular separation
of the planet from the star (approximately 1 arc-second) and the long orbital
period make this planet a prime candidate for both direct imaging and
space-based astrometric measurements.
