We report on the discovery and the Rossiter-McLaughlin (R-M) effect of Kepler-8b, a transiting planet identified by the NASA Kepler Mission. Kepler photometry and Keck-HIRES radial velocities yield the radius and mass of the planet around this F8IV subgiant host star. The planet has a radius R P = 1.419 R J and a mass M P = 0.60 M J, yielding a density of 0.26 g cm–3, one of the lowest planetary densities known. The orbital period is P = 3.523 days and the orbital semimajor axis is 0.0483+0.0006 –0.0012 AU. The star has a large rotational vsin i of 10.5 ± 0.7 km s–1 and is relatively faint (V 13.89 mag); both properties are deleterious to precise Doppler measurements. The velocities are indeed noisy, with scatter of 30 m s–1, but exhibit a period and phase that are consistent with those implied by transit photometry. We securely detect the R-M effect, confirming the planet's existence and establishing its orbit as prograde. We measure an inclination between the projected planetary orbital axis and the projected stellar rotation axis of ¿ = –264 ± 101, indicating a significant inclination of the planetary orbit. R-M measurements of a large sample of transiting planets from Kepler will provide a statistically robust measure of the true distribution of spin-orbit orientations for hot Jupiters around F and early G stars