We report the discovery and the Rossiter-McLaughlin 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 RP = 1.419 RJ and a mass, MP = 0.60 MJ, yielding a density of 0.26 g cm^-3, among the lowest density planets known. The orbital period is P = 3.523 days and orbital semima jor axis is 0.0483+0.0006/-0.0012 AU. The star has a large rotational v sin i of 10.5 +/- 0.7 km s^-1 and is relatively faint (V = 13.89 mag), both properties deleterious to precise Doppler measurements. The velocities are indeed noisy, with scatter of 30 m s^-1, but exhibit a period and phase consistent with the planet implied by the photometry. We securely detect the Rossiter-McLaughlin effect, confirming the planets existence and establishing its orbit as prograde. We measure an inclination between the projected planetary orbital axis and the projected stellar rotation axis of lambda = -26.9 +/- 4.6 deg, indicating a moderate inclination of the planetary orbit. Rossiter-McLaughlin 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 in general.