We report the first detection of [C II] 158 mum line emission from the diffuse interstellar medium at high galactic latitude. We have measured the integrated line intensity in a 36' field of view along a triangular scan path in a 5-degrees x 20-degrees region in Ursa Major using a rocket-borne, liquid-helium-cooled spectrophotometer. The scan included high-latitude infrared cirrus, molecular clouds, a bright external galaxy, M82, and the H I Hole, which is a region of uniquely low neutral hydrogen column density. Emission from [C II] is observed in all regions, and, in the absence of appreciable CO emission, it is well correlated with neutral hydrogen column density. We observe a [C II] gas cooling rate which varies from (1.18 +/- 0.4 to 3.25 +/- 0.8) x 10(-26) ergs s-1 H-atom-1, in good agreement with recent observations of UV absorption lines at high galactic latitude. Regions with CO emission have enhanced [C II] line emission over that expected from the correlation with neutral hydrogen column density. We measure a line-to-continuum ratio which varies from I[C II]/lambdaI(lamda) = 0.002 to 0.008 in comparison with the all-sky average of 0.0082 reported by FIRAS, which is heavily weighted toward the Galactic plane.