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 Hipparcos photometry . We found no significant variations in these quantities with the 906-d period . We also re-analyzed the Ca II \lambda 8662 Å 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 Å 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 .