  We report on the detection of a planetary companion in orbit around the
primary star of the binary system $\gamma$ Cephei. High precision radial
velocity measurements using 4 independent data sets spanning the time interval
1981--2002 reveal long-lived residual radial velocity variations superimposed
on the binary orbit that are coherent in phase and amplitude with a period or
2.48 years (906 days) and a semi-amplitude of 27.5 m s$^{-1}$. We performed a
careful analysis of our Ca II H & K S-index measurements, spectral line
bisectors, and {\it Hipparcos} photometry. We found no significant variations
in these quantities with the 906-d period. We also re-analyzed the Ca II
$\lambda$8662 {\AA} measurements of Walker et al. (1992) which showed possible
periodic variations with the ``planet'' period when first published. This
analysis shows that periodic Ca II equivalent width variations were only
present during 1986.5 -- 1992 and absent during 1981--1986.5. Furthermore, a
refined period for the Ca II $\lambda$8662 {\AA} variations is 2.14 yrs,
significantly less than residual radial velocity period. The most likely
explanation of the residual radial velocity variations is a planetary mass
companion with $M$ sin $i$ = 1.7 $M_{Jupiter}$ and an orbital semi-major axis
of $a_2$ $=$ 2.13 AU. This supports the planet hypothesis for the residual
radial velocity variations for $\gamma$ Cep first suggested by Walker et al.
(1992). With an estimated binary orbital period of 57 years $\gamma$ Cep is the
shortest period binary system in which an extrasolar planet has been found.
This system may provide insights into the relationship between planetary and
binary star formation.
