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We report the detection of a Jupiter-mass planet in a 6.838 day orbit around the 1.28 M☉ subgiant HD 185269. The eccentricity of HD 185269b (e = 0.30) is unusually large compared to other planets within 0.1 AU of their stars. Photometric observations demonstrate that the star is constant to ±0.0001 mag on the radial velocity period, strengthening our interpretation of a planetary companion. This planet was detected as part of our radial velocity survey of evolved stars located on the subgiant branch of the H-R diagram—also known as the Hertzsprung gap. These stars, which have masses between 1.2 and 2.5 M☉, play an important role in the investigation of the frequency of extrasolar planets as a function of stellar mass.