Evidence for a Long-period Planet Orbiting Epsilon Eridani

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.